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

Hohti, Aarno; Husek, Miroslav; Pelant, Jan

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

Authors

Hohti, Aarno

Husek, Miroslav

Pelant, Jan

Description

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.
15 pages