Horst Herrlich's publications

Transcription

1 Horst Herrlich's publications A) As Editor Categorical Topology, Mannheim 1975 Lecture Notes Math. 540, Springer 1976 (with E. Binz) 2 Nordwestdeutsches Kategorienseminar, Bremen 1976 Mathematik - Arbeitspapiere 7, Univ. Bremen 1976 (with H.-E. Porst, R.-E. Hoffmann and M.B. Wischnewsky) Categorical Topology, Berlin 1978 Lecture Notes Math. 719, Springer 1979 (with G. Preuss) 4 Structure of Topological Categories, Bremen 1978 Mathematik - Arbeitspapiere 18, Univ. Bremen 1979 (with R.-E. Hoffmann, H.-E. Porst and M.B. Wischnewsky) Special Topics in Topology and Category Theory, Bremen 1981 Mathematik - Arbeitspapiere 25, Univ. Bremen 1981 (with R.-E. Hoffmann, H.-E. Porst and M.B. Wischnewsky) Categorical Topology, Toledo 1983 Heldermann Verlag 1984 (with H.L. Bentley, M. Rajagopalan and H. Wolff) Convergence Structures, Bechyne 1984 Akademie-Verlag, Berlin 1985 (with J. Novak, W. Gahler and J. Mikusinski) Workshop on Category Theory, Bremen 1986 Mathematik-Arbeitspapiere 28, Univ. Bremen 1987 (with R.-E. Hoffmann and H.-E. Porst) 9 Categorical Topology, L'Aquila 1986 Topology and its Applications 27, No. 2 (1987) (with E. Giuli) 313

2 314 HORST HERRLICH Categorical Methods in Computer Science with Aspects from Topology, Berlin 1988 Lecture Notes Computer Science 393, Springer 1989 (with H. Ehrig, H.-J. Kreowski and G. Preufi) Category Theory at Work, Bremen 1990 Heldermann Verlag 1991 (with H.-E. Porst) Recent Developments of General Topology and its Applications, Berlin 1992 Internat. Conf. in Memory of Felix Hausdorff ( ) Akademie Verlag 1992 (with W. Gahler and G. PreuB) Symposium on Categorical Topology, Cape Town 1994 Univ. Cape Town 1999 (with B. Banaschewski and C. Gilmour) CatMAT 2000 Proc. Conf. Cat. Methods in Algebra and Topology Mathematik-Arbeitspapiere Nr. 54, Universitat Bremen 2000 (with H.-E. Porst) B) Mathematical Biography Categorical Topology - The Complete Work of Graciela Salicrup Aportaciones Matematicas 2, Soc. Matem. Mexicana 1988 (with C. Prieto) C) Books Topologische Reflexionen und Coreflexionen Springer Lecture Notes Math. 78 (1968)

3 PUBLICATIONS Category Theory Allyn and Bacon ed. Heldermann Verlag 1979 (with G.E. Strecker) Einfuhrung in die Topologie: Metrische Raume Heldermann Verlag, Berlin 1986 (with H. Bargenda and C. Trompelt) 4 Topologie I: Topologische Raume Heldermann Verlag, Berlin 1986 (with H. Bargenda) Topologie II: Uniforme Raume Heldermann Verlag, Berlin Abstract and Concrete Categories Wiley-Interscience Publ., New York 1990 (with G.E. Strecker and J. Adamek) D) Papers Ordnungsfahigkeit topologischer Raume Thesis, Preie Universitat Berlin Ordnungsfahigkeit zusammenhangender Raume Fund. Math. 57 (1965), Ordnungsfahigkeit total-diskontinuierlicher Raume Math. Annalen 159 (1965), Ty-Abgeschlossenheit und T^-Minimalitat Math. Zeitschrift 88 (1965), Wann sind alle stetigen Abbildungen in Y konstant? Math. Zeitschrift 90 (1965), kompakte Raume Habilitationsschrift, Preie Universitat Berlin Nicht alle T 2 -minimalen Raume sind von 2. Kategorie Math. Zeitschrift 91 (1966), 185

4 316 HORST HERRLICH Quotienten geordneter Raume und Folgenkonvergenz Fund. Math. 61 (1967), Fortsetzbarkeit stetiger Abbildungen und Kompaktheitsgrad topologischer Raume Math. Zeitschrift 96 (1967), kompakte Raume Math. Zeitschrift 96 (1967), Properties which are closely related to compactness Indag. Math. 29 (1967), (with J. van der Slot) Mengen reeller Zahlen. Ordnungstheoretische und topologische Kennzeichnung Prace Math. 11 (1968), On intersections of compact sets Duke Math. J. 35 (1968), ff-closed spaces and reflective subcategories Math. Annalen 117 (1968), (with G.E. Strecker) 15 Strengthening Alexander's subbase theorem Duke Math. J. 35 (1968), (with G.E. Strecker, E. Wattel and J. de Groot) Compactness as an operator Compositio Math. 21 (1969), (with J. de Groot, G.E. Strecker and E. Wattel) 17 Separation axioms and direct limits Canad. Math. Bull. 12 (1969), Limit operators and topological coreflections Trans. Amer. Math. Soc. 146 (1969), Topological coreflections Int. Symp. Topology, Herceg Novi 1968 (Belgrad 1969),

5 PUBLICATIONS On the concept of reflections in general topology Int. Symp. Extension Theory of Top. Structures and Appl., Berlin 1967, (Berlin 1969), An example in category theory Math. Zeitschrift 113 (1970), Factorization of morphisms / : B > A Math. Zeitschrift 114 (1970), Regular-closed, Urysohn-closed, and completely Hausdorff-closed spaces Proc. Amer. Math. Soc. 26 (1970), Coreflective subcategories Trans. Amer. Math. Soc. 157 (1971), (with G.E. Strecker) 25 A characterization of fc-ary algebraic categories Manuscripty Math. 4 (1971), Categorical topology Gen. Topol. Appl. 1 (1971), Algebra n Topology = Compactness Gen. Topol. Appl. 1 (1971), (with G.E. Strecker) Coreflective subcategories in general topology Fund. Math. 73 (1972), (with G.E. Strecker) 29 A generalization of perfect maps 3. Prague Top. Sym., 1971, (Prague 1972), Identities in categories Canad. Math. Bull. 15(2) (1972), (with C.M. Ringel) Perfect subcategories and factorizations Keszthely 1972, (Coll. Math. Soc. G. Bolyai, Top. 1974),

6 318 HORST HERRLICH 32 Regular categories and regular functors Canad. J. Math. 26 (1974), Topological functors Gen. Topol. Appl. 4 (1974), Cartesian closed topological categories Math. Coll. Univ. Cape Town 9 (1974), A concept of nearness Gen. Topol. Appl. 4 (1974), On the extendibility of continuous functions Gen. Topol. Appl. 4 (1974), Topological structures Amsterdam Math Centre Tracts 52 (1974), Topological structures Int. Congr. Math., Vancouver 1974, (Vol. 2, 1975), Epireflective subcategories of Top need to be cowellpowered Comment. Math. Univ. Carolinae 16 (1975), Initial completions Math. Zeitschrift 150 (1976), On the relations P(X xy)=px xpy Gen. Topol. Appl. 6 (1976), (with W.W. Comfort) 42 Extensions of topological spaces Topology (eds. Franklin and Smith Thomas) (Marcel Dekker, New York 1976), Convenient categories for topologists Topology (eds. Franklin and Smith Thomas) (Marcel Dekker, New York 1976), Convenient categories for topologists Comment. Math. Univ. Carolinae 17 (1976), (with H.L. Bentley and W.A. Robertson)

7 PUBLICATIONS Some topological theorems which fail to be true Springer Lecture Notes Math. 540 (1976), Subcategories defined by implications Houston Math. J. 2 (1976), Products in topology Quaestiones Math. 2 (1977), The forgetful functor Cont > Prox is topological Quaestiones Math. 2 (1977), Cartesian closed topological hulls Proc. Amer. Math. Soc. 62 (1977), (with L.D. Nel) The reals and the reals Gen. Topol. Appl. 9 (1978), Reflective Mac Neille completions of fibre-small categories need not be fibre-small Comment. Math. Univ. Carolinae 19 (1978), Completion as reflection Comment. Math. Univ. Carolinae 19 (1978), Completeness is productive Springer Lecture Notes Math. 719 (1979), Completeness for nearness spaces Amsterdam Math. Centre Tracts 115 (1979), Semi-universal maps and universal initial completions Pacific J. Math. 82 (1979), (with G.E. Strecker)

8 320 HORST HERRLICH 56 Least and largest initial completions, I and II Comment. Math. Univ. Carolinae 20 (1979), (with J. Adamek and G.E. Strecker) 57 The structure of initial completions Cahiers Topol. Geom. Diff. 20 (1979), (with J. Adamek and G.E. Strecker) 58 Algebra U Topology Springer Lecture Notes Math. 719 (1979), (with G.E. Strecker) 59 Initial and final completions Springer Lecture Notes Math. 719 (1979), Dispersed factorization structures Canad. J. Math. 31 (1979), (with G. Salicrup and R. Vazquez) 61 Light factorization structures Quaestiones Math. 3 (1979), (with G. Salicrup and R. Vazquez) 62 Local compactness and simple extensions of discrete spaces Proc. Amer. Math. Soc. 77 (1979), (with V. Kannan and M. Rajagopalan) Equivalence of topologically-algebraic and semitopological functors Canad. J. Math. 32 (1980), (with R. Nakagawa, G.E. Strecker and T. Titcomb) Orderability of connected graphs and nearness spaces Amsterdam Math. Centre Tracts 142 (1981), Topicos de Categorias Topologicas y Algebraicas Univ. Santiago de Chile Universal completions of concrete categories Springer Lecture Notes Math. 915 (1982),

9 PUBLICATIONS The coreflective hull of the contigual spaces in the category of merotopic spaces Springer Lecture Notes Math. 915 (1982), What is algebra? What is topology? Topology, Spec. Seminar Mexico 3 (1982), Inside Top Durand Math. Assoc (Me Master Univ. 1983), Are there convenient subcategories of Top? Topol. Appl. 15 (1983), Categorical topology General Topology and its Relations to Modern Analysis and Algebra 5 Proc. Fifth Prague Topol. Symp. 1981, (Heldermann Verlag 1983), The quasicategory of quasispaces is illegitimate Archiv Math. 40 (1983), (with M. Rajagopalan) Products of quotients in Near Topol. Appl. 17 (1984), alias: Y.T. Rhineghost, 74 Graciela Salicrup - her mathematical work Categorical Topology (eds. Bentley, Herrlich, Rajagopalan and Wolff) (Heldermann Verlag 1984), Universal topology Categorical Topology (eds. Bentley, Herrlich, Rajagopalan and Wolff) (Heldermann Verlag 1984),

10 322 HORST HERRLICH 76 Topological structure theory Convergence Struct. Appl., Schwerin 1983 (Akademie Verlag 1984), Sequential structures: categorical aspects Convergence Structures (eds. Novak, Gahler, Herrlich and Mikusinski) (Akademie Verlag 1985), Ascoli's theorem for a class of merotopic spaces Convergence Structures (eds. Novak, Gahler, Herrlich and Mikusinski) (Akademie Verlag 1985), Filter convergence via sequential convergence Comment. Math. Univ. Carolinae 27 (1986), (with R. Beattie and H.P. Butzmann) 80 Cartesian closed categories, quasitopoi, and topological universes Comment. Math. Univ. Carolinae 27 (1986), (with J. Adamek) 81 Topological structures and injectivity Rendiconti di Palermo 12 (1986), Essentially algebraic categories Quaestiones Math. 9 (1986), Cartesian closed topological hulls as injective hulls Quaestiones Math. 9 (1986), (with G.E. Strecker) 84 Concrete categories and injectivity Springer Lecture Notes Comp. Sci. 239 (1986), (with H. Bargenda and G.E. Strecker) 85 Galois connections Springer Lecture Notes Comp. Sci. 239 (1986), (with M. Husek)

11 PUBLICATIONS The category of Cauchy spaces is cartesian closed Topol. Appl. 27 (1987), (with H.L. Bentley and E. Lowen-Colebunders) 87 Topological improvements of categories of structures sets Topol. Appl. 27 (1987), Factorizations, denseness, separation, and relatively compact objects Topol. Appl. 27 (1987), (with G. Salicrup and G.E. Strecker) 89 Kategorientheorie Mathematikstudium? In Bremen? Na klar! Fachbereich Mathematik und Informatik, Univ. Bremen 1987, Hereditary topological constructs General Topology and its Relations to Analysis and Algebra 6 Proc. Sixth Prague Topol. Symp (Heldermann Verlag 1988), On the representability of partial morphisms in Top and in related constructs Springer Lecture Notes Math (1988), Essentially equational categories Cahiers Topol. Geom. Diff. Categ. 29 (1988), (with J. Adamek and J. Rosicky) 93 Sequential structures induced by merotopies Comment. Math. Univ. Carolinae 29 (1988), Realizations of topologies and closure operators by set systems and neighbourhoods Archivum Math. (Brno) 25 (1989), Monadic decompositions J. Pure Appl. Algebra 59 (1989), (with J. Adamek and W. Tholen)

12 324 HORST HERRLICH 96 The construct PRO of projection spaces: its internal structure Springer Lecture Notes Comp. Sci. 393 (1989), (with H. Ehrig) 97 Functors lifting limits Categorical Topology (eds. Adamek and Mac Lane) World Scientific, Singapore 1989, Completeness almost implies cocompleteness Categorical Topology (eds. Adamek and Mac Lane) World Scientific, Singapore 1989, (with J. Adamek and J. Reiterman) 99 Zero sets and complete regularity for nearness spaces Categorical Topology (eds. Adamek and Mac Lane) World Scientific, Singapore 1989, (with H.L. Bentley and R.G. Ori) A characterization of concrete quasitopoi by injectivity J. Pure Appl. Algebra 68 (1990), 1-9 (with J. Adamek) 101 Convergence J. Pure Appl. Algebra 68 (1990), (with H.L. Bentley and E. Lowen-Colebunders) 102 Galois connections categorically J. Pure Appl. Algebra 68 (1990), (with M. Husek) 103 Remarks on categories of algebras defined by a proper class of operations Quaestiones Math. 13 (1990), Improving constructions in topology Category Theory at Work (eds. Herrlich and Porst) (Heldermann Verlag 1991), 1-20 (with H.L. Bentley and R. Lowen)

13 PUBLICATIONS Improving Top: PrTop and PsTop Category Theory at Work (eds. Herrlich and Porst) (Heldermann Verlag 1991), (with E. Lowen-Colebunders and F. Schwarz) 106 Algebra U Topology Category Theory at Work (eds. Herrlich and Porst) (Heldermann Verlag 1991), (with T. Mossakowski and G.E. Strecker) Convenient topological constructs Applications of Category Theory to Fuzzy Subsets (eds. Rodabaugh, Klement and Hohle) Kluwer Acad. Publ. 1992, Epireflections which are completions Cahiers Topolog. Geom. Diff. Categ. 33 (1992), (with G.C.L. Brummer and E. Giuli) 109 Hyperconvex hulls of metric spaces Topology and Appl. 44 (1992), Compactness = completeness n total boundedness - a natural example of a non-reflective intersection of reflective subcategories Recent Developments of General Topology and its Applications (eds. Gahler, Herrlich and Preufi) Akademie Verlag 1992, (with M. Husek) 111 Categorical topology Recent Progress in General Topology (eds. Husek and van Mill) Elsevier Sci. Publ. 1992, Ch. 11, (with M. Husek) Almost reflective subcategories of Top Topology and Appl. 49 (1993),

14 326 HORST HERRLICH 113 Some open categorical problems in Top Appl. Categ. Struct. 1 (1993), 1-19 (with M. Husek) 114 Compact T 0 -Spaces and Tb-Compactifications Appl. Categ. Struct. 1 (1993), On the failure of Birkhoff's Theorem for locally small based equational categories of algebras Cahiers Topol. Geom. Diff. Categ. 34 (1993), Factorization of flows and completeness of categories Quaestiones Math. 17 (1994), 1-11 (with W. Meyer) 117 Essential extensions of Hausdorff spaces Appl. Categ. Struct. 2 (1994), A Baire Category Theorem for quasi-metric spaces Indian J. Math. 37 (1995), (with H.L. Bentley and W.N. Hunsaker) Compactness and the Axiom of Choice Appl. Categ. Struct. 3 (1995), An effective construction of a free z-ultrafilter Papers on Gen. Topology and Appl. 11-th Summer Conf. Univ. Southern Maine (eds. S. Andima, R.C. Flagg, G. Itzkovitz, Y. Kong, R. Kopperman, and P. Misra) Annals New York Acad. Sci. 806 (1996), Categorical Topology - its origins, as exemplified by the unfolding of the theory of topological reflections and coreflections before 1971 Handbook of the History of General Topology (eds. C.E. Aull and R. Lowen), Kluwer Acad. Publ. Vol. 1 (1997), (with G.E. Strecker) 122 When is N Lindelof? Comment. Math. Univ. Carolinae 38 (1997), (with G.E. Strecker)

15 PUBLICATIONS Choice principles in elementary topology and analysis Comment. Math. Univ. Carolinae 38 (1997), The Ascoli Theorem is equivalent to the Boolean Prime Ideal Theorem Rostock Math. Kolloq. 51 (1997), Stabilitat topologischer Eigenschaften unter kategoriellen Konstruktionen Mathematik aus Berlin (edt. H.G.W. Begehr) Weidler-Verlag Berlin 1997, The Ascoli Theorem is equivalent to the Axiom of Choice Seminarberichte FB Mathematik Univ. Hagen 62 (1997), Maximal filters, continuity and choice principles Quaestiones Math. 20 (1997), (with J. Steprans) Morita-extensions and nearness-completions Topol. Appl. 82 (1998), Doitchinov's construct of supertopological spaces is topological Serdica Math. J. 24 (1998), The historical development of uniform, proximal, and nearness concepts in topology Handbook of the History of General Topology (eds. C.E. Aull and R. Lowen), Kluwer Acad. Publ. Vol. 2 (1998), (with H.L. Bentley and M. Husek) 131 Countable choice and pseudometric spaces Topology and Appl. 85 (1998),

16 328 HORST HERRLICH 132 Categorical properties of probabilistic convergence spaces Appl. Categ. Struct. 6 (1998), (with Dexue Zhang) Compactness and rings of continuous functions - without the axiom of choice Proc. Symp. Cat. Topology, Cape Town 1994, Univ. Cape Town 1999 (eds. B. Banaschewski, C.R.A. Gilmour, and H. Herrlich), On simultaneously reflective and coreflective subconstructs Proc. Symp. Cat. Topology, Cape Town 1994, Univ. Cape Town 1999 (eds. B. Banaschewski, C.R.A. Gilmour, and H. Herrlich), (with R. Lowen) 135 Composing special epimorphisms and retractions Cahiers Topol. Geom. Diff. Cat. 40 (1999), (with L. Schroder) 136 Productivity of coreflective classes of topological groups Comment. Math. Univ. Carolinae 40 (1999), (with M. Husek) 137 Products, the Baire category theorem, and the axiom of choice Comment. Math. Univ. Carolinea 40 (1999), (with K. Keremedis) 138 Weak separatedness for nearness spaces Indian J. Math. 41 (1999), (with D. Vaughan) 139 Powers of 2 Notre Dame Journal of Formal Logic 40 (1999), (with K. Keremedis) Generating ordered topological spaces from LOTS Topol. Appl. 105 (2000), (with E. Kronheimer)

17 PUBLICATIONS Nearness, subfitness and sequential regularity Appl. Categ. Structures 8 (2000), (with A. Putlr) 142 Free adjunctions of morphisms Appl. Categ. Structures 8 (2000), (with L. Schroder) 143 Abstract Initiality Comment. Math. Univ. Carolinae 41 (2000), (with L. Schroder) 144 The Baire Category Theorem and Choice Topol. Appl. 108 (2000), (with K. Keremedis) 145 On countable products of finite Hausdorff spaces Math. Logic Quart. 46 (2000), (with K. Keremedis) On the strict completion of a nearness space Quaestiones Math. 24 (2001), Is the construct of L-topological spaces a co-tower extension of some simpler construct? Quaestiones Math. 24 (2001), (with D. Zhang) 148 The functor that wouldn't be Categorical Perspectives (eds. J. Koslowski and A. Melton) Birkhauser, 2001, The emergence of functors Categorical Perspectives (eds. J. Koslowski and A. Melton) Birkhauser, 2001, 37-45

18 330 HORST HERRLICH 150 The naturals are Lindelof iff Ascoli holds Categorical Perspectives (eds. J. Koslowski and A. Melton) Birkhauser, 2001, Abelian groups: simultaneously reflective and coreflective subcategories versus modules Categorical Perspectives (eds. J. Koslowski and A. Melton) Birkhauser, 2001, Free factorizations Appl. Categ. Structures 9 (2001), (with L. Schroder) Weak factorization systems and topological functors Appl. Categ. Structures 10 (2002), (with J. Adamek, J. Rosicky, and W. Tholen) 154 Products of Lindelof T% spaces are Lindelof - in some models of ZF Comment. Math. Univ. Carolinae 43 (2002), A characterization of the prime closed filter compactification of a topological space Quaestiones Math. 25 (2002), On a generalized small-object argument for the injective subcategory problem Cahiers topol. geom. diff. categ. 43 (2002), (with J. Adamek, J. Rosicky, and W. Tholen) (with J. Adamek, J. Rosicky, and W. Tholen) 157 Zum Begriff des topologischen Raumes In: Felix Hausdorff: Gesammelte Werke, Bd. II, Springer 2002, (with M. Epple, M. Husek, G. Preufi, W. Purkert, and E. Scholz 158 Trennungsaxiome In: Felix Hausdorff: Gesammelte Werke, Bd. II, (with M. Husek and G. Preufi)

19 PUBLICATIONS Zusammenhang In: Felix Hausdorff: Gesammelte Werke, Bd. II, (with M. Husek and G. Preufi) 160 Abzahlbarkeitsaxiome In: Felix Hausdorff: Gesammelte Werke, Bd. II, (with M. Husek and G. Preufi) 161 Hausdorff-Metriken und Hyperraume In: Felix Hausdorff: Gesammelte Werke, Bd. II, (with M. Husek and G. Preufi) 162 Vervollstandigung und totale Beschranktheit In: Felix Hausdorff: Gesammelte Werke, Bd. II, (with M. Husek and G. Preufi) 163 Striking differences between ZF and ZF+ weak choice in view of metric spaces Quaestiones Math. 25 (2002), (with K. Keremedis and E. Tachtsis) 164 The Boolean prime ideal theorem holds iff maximal open niters exist Cahiers topol. geom. diff. categ. 43 (2002), alias Y.T. Rhineghost (with K. Keremedis and E. Tachtsis) 165 Injective hulls are not natural Algebra Universalis 48 (2002) (with J. Adamek, J. Rosicky, and W. Tholen) The axiom of choice holds iff maximal closed niters exist Math. Logic Quarterly 49 (2003), Merotopological spaces Appl. Categ. Struct. 12 (2004) (with H. L. Bentley) 168 On closure operators, the reals, and choice (with E. Giuli) [to appear]

20 332 HORST HERRLICH 169 Zur Existenz maximaler Filter und Ideale [to appear] 170 On the epireflective hull of Top in Near (with H. L. Bentley and J. Carlson) [to appear]

21 Fur HH, von BB, nach CM Palmstrom mochte gerne horen wie das Unendliche zu denken sei: dass Mengen der Zahl eins, zwei, drei und soweiter, dazu nicht gehoren steht natiirlich vollig fest? und drum unendlich sicher ist alles was jene nach sich lasst. Aber wie ist nun das Leere zu verstehn? Palmstrom kann hier nicht umhin auch einen Hauch Unendlichens zu sehn? jedoch v. Korf doziert mit Strenge: Nein, "nichts" ist eine endliche Menge. Tertium Non Datur Korf und Palmstro kamen zu erwagen ob und wie das ausgeschloss'ne Dritte zu begriinden sei. Sollte wohl das Zweierlei ein vollig unanriittelbarer Zug jedweden Wissens sein, oder ist das schlichte "Ja-vel-Nein" doch durch subtilere Prinzipien zu ersetzen? Korf lehnt eher erst'rem zu, diese Richtung vorgewiesen glaubend durch manche wichtige Autoritat: siehe Aristoteles und Boole. Palmstrom ist dem weniger gewogen, ahnt formalen Kurzschluss hier, verstossend gegen konstruktive Wirklichkeit, und er formuliert die Bitte: ach, gewahrt mir doch das Dritte. 333