一些函数空间的完备性

General Topology and its Applications Pub Date : 1978-11-01 DOI:10.1016/0016-660X(78)90027-2

Surjit Singh Khurana

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引用次数: 0

摘要

证明了如果X是序紧Hausdorff空间，E是Hausdorff完备一致空间，C(X, E)是X上所有具有C一致性的E值连续函数的空间，C是X的所有紧子集的类，H是C(X, E)的闭子集，其中包含C(X, E)的预紧子集的可数并集，则H是完备的。

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A completeness property of some function spaces

It is proved that if X is a sequentially compact Hausdorff space, E a Hausdorff complete uniform space, C(X, E) the space of all E-valued continuous functions on X with $C$ uniformity, $C$ being the class of all compact subsets of X, and H a closed subset of C(X, E) containing a countable union of precompact subsets of C(X, E) as a dense subset, then H is complete.

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General Topology and its Applications

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