Local and Strong Local Paracompactness

Abstract

<p> This thesis gives basic properties of the newly defined topological properties local paracompactness and strong local paracompactness. An example is given to show that they do not coincide in T2 spaces; another example is given of a strongly locally paracompact T2 space which is neither locally compact nor paracompact. The existence of a one point paracompactification analagous to the Aleksandrov one point compactification is constructed and proved for strongly locally paracompact T2 spaces. Also considered are conditions under which these two properties are preserved under closed maps and heredity.</p>