On products of \(k\)-spaces (Q1763623)

It is well known that every product of a locally compact space with a \(k\)-space is a \(k\)-space. In the paper under review, characterizations of a \(k\)-space \(X\) are discussed such that \(X\times Y\) is a \(k\)-space for every space \(Y\) in some class of \(k\)-spaces. For example, it is shown that \(X\) is locally compact if and only if \(X\times Y\) is a \(k\)-space for every quotient compact image \(Y\) of a locally compact, paracompact space.