Uniform Eberlein compactifications of metrizable spaces Academic Article uri icon

abstract

  • Abstract We prove that each metrizable space X (of size| X|⩽ c) 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 A of compact spaces, which contains the empty set, the singleton, and is closed under producing the Alexandroff compactification of the topological sum of a family of compacta from the class A.

publication date

  • January 1, 2012