Continuous function spaces, (db)-spaces and strongly Hewitt spaces

Topology and its Applications

Volumn 141, Issue 1-3, 2004, Pages 171-186

  Todd, Aaron R ^a   Render, Hermann ^b  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Bairelike; Barrelled; Continuous function spaces; Property (db); Realcompact; Strongly Hewitt; Suprabarrelled; Unordered Bairelike

Indexed keywords

EID: 2342453261     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2003.12.005     Document Type: Article

References (35)

1. Abramovich Y.A. Kitover A.K. Inverses of Disjointness Preserving Operators Mem. Amer. Math. Soc. vol. 679 2000 American Mathematical Society Providence, RI
2. Aranjo J. Beckenstein E. Narici L. When is a separating map biseparating? Arch. Math. 67 1996 395-407
3. p-theory Questions Answers Gen. Topology 4 1987 1-109
4. Arhangel'skii A.V. Topological Function Spaces Math. Appl. 1992 Kluwer Academic Dordrecht
5. Baumgartner J.E. van Douwen E.K. Strong realcompactness and weakly measurable cardinals Topology Appl. 35 1990 239-251
6. H. Buchwalter, Parties bornées d'un espace topologique complètement régulier, in: Sém. Choquet, 9e année 1969-1970 Fasc. 2 14, Paris, 1970
7. de Wilde M. Schmets J. Characterisation des espace C(X) ultrabornologiques Bull. Soc. Roy. Sci. Liège 41 1972 268 271
8. Dunford N. Schwartz J.T. Linear Operators I 1967 Interscience New York-
9. Gillman L. Jerison M. Rings of Continuous Functions 1976 Springer Berlin
10. Horvath J. Topological Vector Spaces and Distributions, vol. I 1966 Addison-Wesley Reading, MA
11. Jarchow H.J. Locally Convex Spaces 1981 Teubner Stuttgart
12. J. Ka̧kol, Personal communication, 5/2001
13. Ka̧kol J. Śliwa W. Strongly Hewitt spaces Topology Appl. 119 2002 219-227
14. c(T), Dissertation, Ludwig-Maximilians-Universität, München, 1978
15. Nachbin L. Topological vector spaces of continuous functions Proc. Nat. Acad. Sci. USA 40 1954 471-474
16. Pełczyński A. Linear extensions, linear averagings and their applications to linear topological classification of spaces of continuous functions Dissertationes Mat. 58 1968
17. Pérez Carreras P. Bonet J. Barrelled Locally Convex Spaces North-Holland Math. Stud. vol. 131 1987 North-Holland Amsterdam
18. Render H. On the property (db) for continuous function spaces Topology Appl. 92 1999 101-106
19. Render H. Corrigendum to [18] Topology Appl. 111 2001 371
20. Robertson A.P. Robertson W.J. Topological Vector Spaces Cambridge Tracts in Math. Math. Phys. vol. 53 1964 Cambridge University Press Cambridge
21. Robertson W.J. Tweddle I. Yeomans F.E. On the stability of barrelled topologies, III Bull. Austral. Math. Soc. 22 1981 99-112
22. W. Roelcke, Increasing sequences of absolutely convex sets, Cambridge talk 1970 cited in [14]
23. Sánchez Ruiz L.M. Saxon S.A. Weak barrelledness conditions in: Brokate M. Siddiqi A.H. (Eds.), Functional Analysis with Current Applications in Science, Technology and Industry Pitman Res. Notes Math. Ser. vol. 377 1998 20-36 Longman Harlow
24. Saxon S.A. Nuclear and product spaces, Bairelike spaces and the strongest locally convex topology Math. Ann. 197 1972 87-106
25. Saxon S.A. Narayanaswami P.P. Metrizable (LF)-spaces, (db)-spaces and the separable quotient problem Bull. Australian Math. Soc. 23 1 1981 65-80
26. Schmets J. Espaces de Fonctions Continues Lecture Notes in Math. vol. 519 1976 Springer Berlin
27. Schmets J. Spaces of Vector-Valued Continuous Functions Lecture Notes in Math. vol. 1003 1983 Springer Berlin
28. Semadeni Z. Banach Spaces of Continuous Functions, vol. I 1971 PWN Warszawa
29. Shirota T. On locally convex vector spaces of continuous functions Proc. Japan Acad. 30 1954 294-298
30. κ(X) and a property of (db)-spaces Ann. Mat. Pura Appl. (IV) 128 1981 317-323
31. A.R. Todd, H. Render, Continuous function spaces and the locally convex property (db), Abstract No. 966-46-166, AMS 966th Meeting, Stevens Institute, Hoboken, NJ, April 29, 2001
32. Todd A.R. Saxon S.A. A property of locally convex Baire spaces Math. Ann. 206 1973 23-34
33. Valdivia M. On certain barrelled normed spaces Ann. Inst. Fourier Grenoble 29 3 1979 39-56
34. Valdivia M. On suprabarrelled spaces in: Machado S. (Ed.), Functional Analysis, Holomorphy, and Approximation Theory Lecture Notes in Math. vol. 843 1981 572-580 Springer Berlin
35. Warner S. The topology of compact convergence on continuous function spaces Duke Math. J. 25 1958 265-282