Characterisation of compactness through convergence in Tychonoff spaces

Abstract

In this article we first give a characterisation of compact spaces among T 3.5 T_{3.5} spaces by improving a theorem of J. Ewert. Then, with the aid of a new type of convergence, we give a characterisation of the pseudocompact and of the Lindelöf T 3.5 T_{3.5} spaces.