A Note on the Completeness of Cc(X,Y)
Functional Analysis
2010-04-09 v1
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.
Keywords
Cite
@article{arxiv.1004.1365,
title = {A Note on the Completeness of Cc(X,Y)},
author = {Jan Harm van der Walt},
journal= {arXiv preprint arXiv:1004.1365},
year = {2010}
}