Uniform Eberlein compactifications of metrizable spaces

Details Uniform Eberlein compactifications of metrizable spaces Uniform Eberlein compactifications of metrizable spaces

2010-12-04

arxiv.org/abs/1012.0920v1

Mathematics

General Topology

6 pages

Scientific paper

We prove that each metrizable space (of cardinality less or equal to continuum) has a (first countable) uniform Eberlein compactification and each scattered metrizable space has a scattered hereditarily paracompact compactification. Each compact scattered hereditarily paracompact space is uniform Eberlein and belongs to the smallest class of compact spaces, that contain the empty set, the singleton, and is closed under producing the Aleksandrov compactification of the topological sum of a family of compacta from that class.

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