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Keywords:
$k$-space; sequential space; strongly Fr'{e}chet space; bi-$k$-space; strongly sequential space; Tanaka space
Summary:
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.
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