Networks for the weak topology of Banach and Fréchet spaces

Journal of Mathematical Analysis and Applications

Volumn 432, Issue 2, 2015, Pages 1183-1199

  Gabriyelyan, S ^a   Kakol, J ^b,c   Kubis W ^c,d   Marciszewski, W ^e  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b ADAM MICKIEWICZ UNIVERSITY   (Poland)

^c MATHEMATICAL INSTITUTE   (Czech Republic)

^d JAN KOCHANOWSKI UNIVERSITY   (Poland)

^e UNIVERSITY OF WARSAW   (Poland)

Author keywords

Fr chet space; Space of continuous functions; Weakly locally convex space; space; 0 space

Indexed keywords

EID: 84939270863     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2015.07.037     Document Type: Article

References (28)

1. Arens R. A topology for spaces of transformations. Ann. of Math. 1946, 47:480-495.
2. Banakh T.O., Bogachev V.I., Kolesnikov A.V. k*-Metrizable spaces and their applications. J. Math. Sci. (N. Y.) 2008, 155:475-522.
3. Banakh T., Zdomskyy L. The topological structure of (homogeneous) spaces and groups with countable cs*-character. Appl. Gen. Topol. 2004, 5:25-48.
4. Bierstedt K.D., Bonet J. Density conditions in Fréchet and (DF)-spaces. Rev. Mat. Complut. 1989, 2:59-75.
5. Bierstedt K.D., Bonet J. Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 2003, 97:159-188.
6. Cascales B., Orihuela J. A biased view of topology as a tool in functional analysis. Recent Progress in Topology III 2014, 93-165. Springer. K.P. Hart, J. van Mill, P. Simon (Eds.).
7. Corson H.H. The weak topology of a Banach space. Trans. Amer. Math. Soc. 1961, 101:207-230.
8. Diestel J., Morris S.A., Saxon S.A. Varieties of linear topological spaces. Trans. Amer. Math. Soc. 1972, 172:207-230.
9. Edgar G.A., Wheeler R.F. Topological properties of Banach spaces. Pacific J. Math. 1984, 115:317-350.
10. Engelking R. General Topology 1989, Heldermann Verlag, Berlin.
11. Fabian M., Habala P., Hájek P., Montesinos V., Pelant J., Zizler V. Functional Analysis and Infinite-Dimensional Geometry. CMS Books Math./Ouvrages Math. SMC 2001.
12. Foged L. A non-normal k-and-ℵ space. Topology Appl. 1986, 22:223-240.
13. Gabriyelyan S., Kąkol J., Kubzdela A., Lopez Pellicer M. On topological properties of Fréchet locally convex spaces with the weak topology. Topology Appl. 2015, in press. 10.1016/j.topol.2015.05.075.
14. Gao Z.M. ℵ-space is invariant under perfect mappings. Questions Answers Gen. Topology 1987, 5:271-279.
15. Gruenhage G. Generalized metric spaces. Handbook of Set-Theoretic Topology 1984, 423-501. North-Holland, New York.
16. 0-spaces. Appl. Gen. Topol. 1971, 1:105-110.
17. Jarchow H. Locally Convex Spaces 1981, B.G. Teubner, Stuttgart.
18. Kąkol J., Kubiś W., Lopez-Pellicer M. Descriptive Topology in Selected Topics of Functional Analysis. Dev. Math. 2011, Springer.
19. σ-sets in the weak topology. J. Math. Anal. Appl. 2009, 350:708-722.
20. 0-spaces. J. Math. Mech. 1966, 15:983-1002.
21. Nyikos P.J. Metrizability and Fréchet-Urysohn property in topological groups. Proc. Amer. Math. Soc. 1981, 83:793-801.
22. O'Meara P. A new class of topological spaces 1966, Dissertation, University of Alberta.
23. O'Meara P. A metrization theorem. Math. Nachr. 1970, 45:69-72.
24. O'Meara P. On paracompactness in function spaces with the compact-open topology. Proc. Amer. Math. Soc. 1971, 29:183-189.
25. Pérez Carreras P., Bonet J. Barrelled Locally Convex Spaces. North-Holland Math. Stud. 1987, vol. 131. North-Holland, Amsterdam.
26. Peris A. Quasinormable spaces and the problem of topologies of Grothendieck. Ann. Acad. Sci. Fenn. Ser. A I Math. 1994, 19:167-203.
27. Sakai M. Function spaces with a countable cs*-network at a point. Topology Appl. 2008, 156:117-123.
28. Semadeni Z. Banach Spaces of Continuous Functions. Monogr. Mat. 1971, vol. 55. PWN-Polish Scientific Publishers, Warszawa.