Countably Compact, Countably Tight, Non-Compact Spaces

Abstract

In this work, we will study several examples of countably compact, countably tight, non-compact spaces. After reviewing the important basic notions, we will examine a construction of several such spaces first given by Manes in "Monads in Topology" and will then detail how to construct such spaces using a more direct and explicit topological process. We will then use this new framework to describe several new spaces and to prove several propositions which are much more transparent from this new viewpoint.