Trans-separability in spaces of continuous vector-valued functions

• Autorzy: Khan L. A.
• Języki publikacji: EN

Abstrakty

EN

Let X be a completely regular Hausdorff space and E a Hausdorff topological vector space (TVS). In this note, we study the notion of trans-separability for certain subspaces of Cb(X,E) endowed with the cr-compact-open and some related topologies.

Słowa kluczowe

EN

topological vector spaces; uniform topology; trans-separable spaces

PL

wektory przestrzenne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 3
• Strony: 611--617
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Khan L. A.

• Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah-21589, Saudi Arabia

Bibliografia

• [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. Sei. 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 Frechet-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] J. H. Shapiro, Linear topological properties of the harmonic space hp 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.