DISCRETE SETS AND THE MAXIMAL TOTALLY BOUNDED GROUP TOPOLOGY

[摘要] If G is an Abelian group, then G# is G with its maximal totally bounded group topology. We prove that every A subset-of G# contains a closed (in G#) and discrete subset B such that \B\ = \A\. This answers a question posed by Eric van Douwen. We also present an example of a countable G# having an infinite relatively discrete subset that is not closed.

[发布日期] 1991-03-15