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On spaces of vector-valued continuous functions

Mendoza Casas, José (1983) On spaces of vector-valued continuous functions. Bulletin des sciences Mathematiques, 107 (2). pp. 177-192. ISSN 0007-4497

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Abstract

Let X be a Hausdorff completely regular space and E be a Hausdorff locally convex topological vector space. Then C(X;E) denotes the linear space of the continuous functions on X, with values in E. Previously [C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A596-A598; MR0271712 (42 #6593)], L. Nachbin introduced the topologies τω|A, τλ|A and τδ|A, where A is a subspace of C(X;E). In this paper, the author studies the case when A is a Cb(X)-submodule of C(X;E) (Cb(X) is the linear space of bounded continuous functions on X). He proves that in this case the topologies τω|A and τλ|A coincide with the compact-open topology, and that the topology τδ|A coincides with the compact-open topology coming from the repletion (= realcompactification) of X.

Item Type:Article
Uncontrolled Keywords:Nachbin topologies; space of vector valued continuous functions; compact- open topology
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16890
Deposited On:26 Oct 2012 08:23
Last Modified:13 Nov 2013 17:36

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