ON SEQUENTIAL AND SELECTIVE FEEBLE COMPACTNESS

摘要

We study two subclasses of the class of feebly compact spaces, namely those classes having the properties appearing in the title. Dorantes-Aldama and Shakhmatov in [6] have given a number of conditions equivalent to selective pseudocompactness in the class of Tychonoff spaces and we show here that these condtions are also equivalent, both in the class of Hausdorff spaces and also in a subclass of the class of T-1-spaces. We characterize both maximal selective feeble compactness and maximal sequential pseudocompactness in the class of T-1-spaces and consider the problem of when a Tychonoff space has a sequentially pseudocompact compactification.