On topological properties of Fréchet locally convex spaces with the weak topology

Topology and its Applications

Volumn 192, Issue , 2015, Pages 123-137

  Gabriyelyan, S S ^a   Kakol, J ^b   Kubzdela, A ^c   Lopez Pellicer, M ^d  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b ADAM MICKIEWICZ UNIVERSITY   (Poland)

^c POZNAN UNIVERSITY OF TECHNOLOGY   (Poland)

^d UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

Author keywords

Banach space; K network; Locally convex Fr chet space; Weak topology; 0 space

Indexed keywords

EID: 84928744428     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2015.05.075     Document Type: Article

References (40)

1. Arkhangel'skii A.V. The frequency spectrum of a topological space and the classification of spaces. Dokl. Akad. Nauk SSSR 1972, 206:1185-1189.
2. Arkhangel'skii A.V. General Topology III. Encyclopedia of Math. Sciences 1991, vol. 51. Springer.
3. *-metrizable spaces and their applications. J. Math. Sci. (N.Y.) 2008, 155:475-522.
4. Barroso C.S., Kalenda O.F.K., Lin P.K. On the approximate fixed point property in abstract spaces. Math. Z. 2012, 271:1271-1285.
5. Bierstedt K.D. An introduction to locally convex inductive limits. Functional Analysis and Its Applications 1988, 33-135. World Sci. Publ., Singapore.
6. Bierstedt K.D., Bonet J. Density conditions in Fréchet and (DF)-spaces. Rev. Mat. Complut. 1989, 2:59-75.
7. Bierstedt K.D., Bonet J. Some aspects of the modern theory of Fréchet spaces. RACSAM Rev. R. Acad. Cienc. Ser. A Mat. 2003, 97:159-188.
8. Christensen J.P.R. Topology and Borel Structure. North-Holland Mathematics Studies 1974, vol. 10. North-Holland, Amsterdam.
9. Cascales B., Orihuela J. On compactness in locally convex spaces. Math. Z. 1987, 195:365-381.
10. Cascales B., Orihuela J. A biased view of topology as a tool in functional analysis. Recent Progress in General Topology III 2014, 93-165. Atlantis Press.
11. Cascales B., Kakol J., Saxon S.A. Metrizability vs. Fréchet-Urysohn property. Proc. Am. Math. Soc. 2003, 131:3623-3631.
12. Cascales B., Orihuela J., Tkachuk V. Domination by second countable spaces and Lindelöf σ-property. Topol. Appl. 2011, 158:204-214.
13. Chasco M.J., Martín-Peinador E., Tarieladze V. A class of angelic sequential non-Fréchet-Urysohn topological groups. Topol. Appl. 2007, 154:741-748.
14. Diestel J. Sequences and Series in Banach Spaces 1984, Springer, New York.
15. Engelking R. General Topology 1978, Heldermann, Berlin.
16. c(X). Georgian Math. J. 2013, 20:247-254.
17. Ferrando J.C., Kakol J., Lopez-Pellicer M. A characterization of trans-separable spaces. Bull. Belg. Math. Soc. Simon Stevin 2007, 14:493-498.
18. Floret K. Weakly Compact Sets. Lecture Notes in Math. 1980, vol. 801. Springer, Berlin.
19. Foged L. Characterization of ℵ-spaces. Pac. J. Math. 1984, 110:59-63.
20. Gabriyelyan S., Kakol J., Leiderman A. On topological groups with a small base and metrizability. Fundam. Math. 2015, 229:129-158.
21. Gabriyelyan S., Kakol J., Leiderman A. The strong Pytkeev property for topological groups and topological vector spaces. Monatshefte Math. 2014, 175:519-542.
22. Gruenhage G. Generalized metric spaces. Handbook of Set-Theoretic Topology 1984, 423-501. North-Holland, New York.
23. 0-spaces. Appl. Gen. Topol. 1971, 1:105-110.
24. Horváth J. Topological Vector Spaces and Distributions, I 1966, Addison-Wesley, Reading, Mass.
25. Jarchow H. Locally Convex Spaces 1981, B.G. Teubner, Stuttgart.
26. Kakol J., Kubiś W., Lopez-Pellicer M. Descriptive Topology in Selected Topics of Functional Analysis. Developments in Mathematics 2011, vol. 24. Springer.
27. 1 have weak approximate fixed point property. J. Math. Anal. Appl. 2011, 373:134-137.
28. Köthe G. Topological Vector Spaces I 1983, Springer-Verlag, Berlin/Heidelberg, New York.
29. McCoy R.A., Ntantu I. Topological Properties of Spaces of Continuous Functions. Lecture Notes in Math. 1988, vol. 1315.
30. 0-spaces. J. Math. Mech. 1966, 15:983-1002.
31. Michael E. A quintuple quotient quest. Gen. Topol. Appl. 1972, 2:91-138.
32. Morris P.D., Wulbert D.E. Functional representation of topological albebras. Pac. J. Math. 1967, 22:323-337.
33. O'Meara P. A metrization theorem. Math. Nachr. 1970, 45:69-72.
34. Pérez Carreras P., Bonet J. Barrelled Locally Convex Spaces. North-Holland Mathematics Studies 1987, vol. 131. North-Holland, Amsterdam.
35. Rogers C.A., Jayne J.E., Dellacherie C., Topsøe F., Hoffman-Jørgensen J., Martin D.A., Kechris A.S., Stone A.H. Analytic Sets 1980, Academic Press.
36. 1. Funct. Approx. 2014, 50:389-399.
37. Schaefer H.H. Topological Vector Spaces 1966, Macmillan, New York.
38. Tkachenko M. Paratopological and semitopological groups vs topological groups. Recent Progress in General Topology III 2014, 825-882. Atlantis Press.
39. p(X) is dominated by irrationals if and only if it is K-analytic. Acta Math. Hung. 2005, 107:253-265.
40. Valov V. Function spaces. Topol. Appl. 1997, 81:1-22.