Abstract:As is well-known, every product of a locally compact space with a $k$-space is a $k$-space. But, the product of a separable metric space with a $k$-space need not be a $k$-space. In this paper, we consider conditions for products to be $k$-spaces, and pose some related questions.
Keywords: $k$-space, sequential space, strongly Fr\'{e}chet space, bi-$k$-space, strongly sequential space, Tanaka space
AMS Subject Classification: 54D50, 54D55, 54B10, 54B15