The Locally Fine Coreflection and Normal Covers in the Products of Partition-complete Spaces

Details The Locally Fine Coreflection and Normal Covers in the Products of Partition-complete Spaces The Locally Fine Coreflection and Normal Covers in the Products of Partition-complete Spaces

2002-08-23

arxiv.org/abs/math/0208182v1

Mathematics

General Topology

15 pages

Scientific paper

We prove that the countable product of supercomplete spaces having a countable closed cover consisting of partition-complete subspaces is supercomplete with respect to its metric-fine coreflection. Thus, countable products of sigma-partition-complete paracompact spaces are again paracompact. On the other hand, we show that in arbitrary products of partition-complete paracompact spaces, all normal covers can be obtained via the locally fine coreflection of the product of fine uniformities.

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