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arXiv · 1004.1365

A Note on the Completeness of Cc(X,Y)

Jan Harm van der Walt
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Abstract

It is known that there are complete, Hausdorff and regular convergence vector spaces X and Y such that Lc(X,Y), the space of continuous linear mappings from X into Y equipped with the continuous convergence structure, is not complete. In this paper, we give sufficient conditions on a convergence vector space Y such that Cc(X,Y) is complete for any convergence space X. In particular, we show that this is true for every complete and Hausdorff topological vector space Y.

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Jan Harm van der Walt. 2010-04-07. A Note on the Completeness of Cc(X,Y). https://arxiv.org/abs/1004.1365

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