The product of two normal initially 𝜅-compact spaces

van Douwen, Eric K.

doi:10.1090/S0002-9947-1993-1022170-8

The product of two normal initially $\kappa$-compact spaces
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Trans. Amer. Math. Soc. 336 (1993), 509-521 Request permission

Abstract:

We prove that it is independent from ${\text {ZFC}}$ that for every cardinal $\kappa$ the following statements are equivalent: (a) $\kappa$ is singular; (b) initial $\kappa$-compactness (defined above the introduction) is productive; (c) initial $\kappa$-compactness is finitely productive; and (d) the product of two initially $\kappa$-compact normal spaces is initially $\kappa$-compact. In particular, $\text {MA}$ implies that there are two countably compact normal spaces whose product is not countably compact.

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