[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2008.45.4.681

TRANS-SEPARABILITY IN THE STRICT AND COMPACT-OPEN TOPOLOGIES

Khan, Liaqat Ali (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE KING ABDULAZIZ UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 681-687 More about this Journal

Abstract

We give a characterization of trans-separability for the function spaces ( $C_b(X,\;E)$ , $\beta$ ), (C(X, E), k) and ( $C_b(X,\;E)$ , u) in the case of E any general topological vector space.

Keywords

topological vector spaces; vector-valued function spaces; strict topology; trans-separable spaces;

Citations & Related Records

Times Cited By Web Of Science : 1 (Related Records In Web of Science)
Times Cited By SCOPUS : 1

Reference
Cited By SCOPUS

1	J. R. Isabell, Uniform Spaces, Mathematical Surveys, No. 12 American Mathematical Society, Providence, R.I. 1964
2	L. A. Khan, The strict topology on a space of vector-valued functions, Proc. Edinburgh Math. Soc. (2) 22 (1979), no. 1, 35-41 DOI
3	L. A. Khan, Separability in function spaces, J. Math. Anal. Appl. 113 (1986), no. 1, 88-92 DOI
4	L. A. Khan, Trans-separability in spaces of continuous vector-valued functions, Demonstratio Math. 37 (2004), no. 3, 611-617
5	V. Klee, Shrinkable neighborhoods in Hausdorff linear spaces, Math. Ann. 141 (1960), 281-285 DOI
6	M. Krein and S. Krein, On an inner characteristic of the set of all continuous functions defined on a bicompact Hausdorff space, C. R. (Doklady) Acad. Sci. URSS (N.S.) 27 (1940), 427-430
7	R. C. Buck, Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95-104 DOI
8	S. A. Choo, Separability in the strict topology, J. Math. Anal. Appl. 75 (1980), no. 1, 219-222 DOI
9	L. Drewnowski, Another note on Kalton's theorems, Studia Math. 52 (1974/75), 233-237
10	L. A. Khan, Generalized separability in vector-valued function spaces, Ann. Univ. Sci. Budapest. Eotvos Sect. Math. 42 (1999), 3-8
11	J. C. Ferrando, J. Kakol, and M. Lopez Pellicer, A characterization of trans-separable spaces, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 3, 493-498
12	D. Gulick and J. Schmets, Separability and semi-norm separability for spaces of bounded continuous functions, Bull. Soc. Roy. Sci. Liege 41 (1972), 254-260
13	N. Robertson, The metrizability of precompact sets, Bull. Austral. Math. Soc. 43 (1991), 131-135 DOI
14	A. H. Shuchat, Approximation of vector-valued continuous functions, Proc. Amer. Math. Soc. 31 (1972), 97-103
15	W. H. Summers, Separability in the strict and substrict topologies, Proc. Amer. Math. Soc. 35 (1972), 507-514
16	C. Todd, Stone-Weierstrass theorems for the strict topology, Proc. Amer. Math. Soc. 16 (1965), 654-659
17	L. Waelbroeck, Topological Vector Spaces and Algebras, Lecture Notes in Mathematics, Vol. 230. Springer-Verlag, Berlin-New York, 1971