Products of sequentially 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.