Products of $\mathfrak {m}$-compact spaces

Abstract:

Some results are given on the closure under suitably restricted products of a class of spaces similar to one considered by Z. Frolík and, more recently, by N. Noble. An answer is given to the following question of Gulden, Fleischman, and Weston: Does there exist $\mathfrak {M} > {\aleph _0}$ and an $\mathfrak {M}$-compact space $X$ such that some subset $A$ of $X$ of cardinality $\leqq \mathfrak {M}$ is contained in no compact subset of $X$? It is shown that for every $\mathfrak {M} \geqq {\aleph _0}$ there is a topological group which has this property.