Abstract

First, we prove that the product X × κ of a strong Σ-space X and a cardinal factor κ is (sub)shrinking if and only if it is (sub)normal. Secondly, we prove that a Σ-product of strong Σ-spaces is subshrinking if and only if it is subnormal. This answers a question raised by the author. Moreover, we discuss the subnormality of the product X × κ of a semi-stratifiable space X and a cardinal factor κ. Thus, we can find several similarities between X × κ and Σ-products.

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