Behaviour of topological properties under the effect of perfect mappings

Abstract

This project write-up assumes the reader is familiar with naive set theory and knows as much general topology as one might expect an undergraduate course to cover. Any omitted proofs can be found in reference [l J. A symbol (x) appearing at the end of a proof implies that the proof is accredited to reference [x]. Each chapter is divided into sections. Chapter one introduces and reviews perfect mappings and some of their properties. In chapter two the properties of separation and compactness are discussed while paracompactness properties are discussed in chapter three. Chapter four deals with the properies of connectedness and others considered basic to the study of general topology. The last section of this chapter comprises of a concluding remark and a tabular summary of all the properties discussed. A total of twenty seven topological properties are covered in the whole project.