On sequentially compact T2 compactifications

Abstract

It is known that a compact space can fail to be sequentially compact. In this paper we consider the following problem: when does a space admit a sequentially compact T2 compactification? In the first section we develop a method to produce such compactifications, and we apply it in the second section to study the question using coverings. Moreover, we obtain solutions for locally compact T2 spaces, and for metrizable spaces.