Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-21T16:55:49.700Z Has data issue: false hasContentIssue false
  • English
  • Français

Strict Topology on Paracompact Locally Compact Spaces

Published online by Cambridge University Press:  20 November 2018

Surjit Singh Khurana
Surjit Singh Khurana*
Affiliation:
The University of Iowa, Iowa City, Iowa
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, X denotes a Hausdorff paracompact locally compact space, E a Hausdorff locally convex space over K, the field of real or complex numbers (we call the elements of K scalars), a filtering upwards family of semi-norms on E generating the topology of E, Cb(X) the space of all continuous scalar-valued funcions on X, and Cb(X, E) the space of all continuous, bounded E-valued functions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 1 , 01 February 1977 , pp. 216 - 219
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Conway, J. B., The strict topology and compactness in the space of measures, Trans. Amer. Math. Soc. 126 (1967), 474–486.Google Scholar
2. Fontenot, R. A., Strict topologies for vector-valued junctions, Can. J. Math. 26 (1974), 841–89)3.Google Scholar
3. Katsaras, A. K., Spaces of vector measures, Trans. Amer. Math. Soc. 206 (1975), 313–328.Google Scholar
4. Khurana, S. S., Convergent sequences of regular measures, Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys. 24 (1976), 37–42.Google Scholar
5. Pryce, J. D., A device of R. J. Whitley applied to pointwise compactness in spaces of continuous functions, Proc. London Math. Soc. 23 (1971), 032–546.Google Scholar
6. Schaeifer, H. H., Topological vector spaces (Macmillan, New York, 1966).Google Scholar
7. Shuchat, A., Integral representation theorems in topological vector spaces, Trans. Amer. Math. Soc. 172 (1972), 373–397.Google Scholar
8. Wells, J., Bounded continuous functions on locally compact spaces, Michigan Math. J. 12 (1965), 119–126.Google Scholar