Products of sequentially pseudocompact spaces

TL;DR

This paper proves that the product of any number of sequentially pseudocompact spaces remains sequentially pseudocompact and establishes the equivalence of different definitions of this property.

Contribution

It demonstrates the stability of sequential pseudocompactness under arbitrary products and clarifies the equivalence of its various definitions.

Findings

Product of sequentially pseudocompact spaces is sequentially pseudocompact

Different definitions of sequential pseudocompactness are equivalent

Extends known results in the topology of pseudocompact spaces

Abstract

We show that the product of any number of sequentially pseudocompact topological spaces is still sequentially pseudocompact. The definition of sequential pseudocompactness can be given in (at least) two ways: we show their equivalence. Some of the results of the present note already appeared in A. Dow, J. R. Porter, R. M. Stephenson, R. G. Woods, Spaces whose pseudocompact subspaces are closed subsets, Appl. Gen. Topol. 5 (2004), 243-264.