Trans-separability in spaces of continuous vector-valued functions

Demonstratio Mathematica

Volumn 37, Issue 3, 2004, Pages 611-617

  Khan, Liaqat Ali ^a  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

Topological vector spaces; Trans separable spaces; Uniform topology; Vector valued continuous functions; compact open topology

Indexed keywords

EID: 39349112582     PISSN: 04201213     EISSN: 23914661     Source Type: Journal    
DOI: 10.1515/dema-2004-0312     Document Type: Article

References (21)

1. B. Cascales and J. Orihuela, On compactness in locally convex spaces, Math. Z. 195(1987), 365-381.
2. L. Drewnowski, An other note on Kalton's Theorem, Studia Math. 52(1975), 233-237.
3. L. Gillman and M. Jerison, Rings of Continuous Functions (Van Nostrand, 1960).
4. D. Gulick, The σ-compact-open topology and its relatives, Math. Scand. 30(1972), 159-176.
5. D. Gulick and J. Schmets, Separability and semi-norm separability for spaces of bounded continuous functions, Bull. Soc. Roy. Sci. Liège 41(1972), 254-260.
6. A. W. Hager, Some nearly fine uniform spaces, Proc. London. Math. Soc. (3) 28(1974), 517-546.
7. J. R. Isabell, Uniform Spaces, Amer. Math. Soc, Providence, 1964.
8. S. O. Iyahen, Semi-convex spaces, Glasgow Math. J. 9(1968), 111-118.
9. L. A. Khan, On seminorm separability for vector-valued function spaces, Studia. Sci. Math. Hungarica 24(1989), 43-45.
10. L. A. Khan, Generalized separability in vector-valued function spaces, Ann. Univ. Sci. Budapest 42(1999), 3-8.
11. L. A. Khan and K. Rowlands, The σ-compact-open topology and its relatives on a space of vector-valued functions, Boll. Un. Mat. Ital. (7) 5-B (1991), 723-739.
12. V. Klee, Lery-Schauder theory without local convexity, Math. Ann. 141(1960), 286-296.
13. M. Krein and S. Krein, On an inner characteristic of the set of all continuous functions on a bicompact Hausdorff space, C. R. (Doklady) Acad. Sci. URSS (N. S.) 27(1940), 423-430.
14. H. Pfister, Bemerkungen zum Satz über die separabilität der Fréchet-Montel-Räume, Arch. Math. 27(1976), 86-92.
15. N. Robertson, The metrizability of precompact sets, Bull. Austral. Math. Soc. 43(1991), 131-135.
16. Z. Semadeni and P. Zbijewski, Spaces of continuous functions I, Studia Math. 16(1957), 130-141.
17. p for 0 < p < 1, Illinois J. Math. 29(1985), 311-339.
18. A. H. Shuchat, Approximation of vector-valued continuous functions, Proc. Amer. Math. Soc. 31(1972), 97-103.
19. L. A. Steen and J. A. Seebach, Jr, Counterexamples in Topology (Springer-Verlag, 1978).
20. W. H. Summers, Separability in the strict and substrict topologies, Proc. Amer. Math. Soc. 35(1972), 507-514.
21. L. Waelbroeck, Topological Vector Spaces and Algebras, Lecture Notes in Math. No. 230, Springer-Verlag, 1971.