ABSTRACT
It is a theorem of Glicksberg that every locally compact Abelian topological group G = < G, t > respects compactness in the sense that a subset A of G is t-compact if and only if A is compact in the topology which G inherits from its Bohr compactification. We give a simple proof of this result for discrete Abelian groups, and we show further that in the obvious sense such groups also respect countable compactness and pseudocompactness. We show also that every discrete Abelian group becomes zero-dimensional in the topology inherited from its Bohr compactification.
AMS classification numbers: 54A05, 20K45, 22B99. Key words and phrases: locally compact Abelian group, totally bounded Abelian group, discrete group, compact space, countably compact space, pseudocompact space, zero-dimensional space, Bohr compactification.
