Date of Award

4-1971

Degree Type

Master's Essay - Restricted

Degree Name

Master of Science (MS)

Department

Mathematical and Statistical Sciences

Abstract

The purpose of this paper is to present a variety of opinions as to which categories of topological spaces should concern algebraic topologists. The desirability for convention on such a question results from the constant necessity of specifying required hypotheses each time a result or construction i s presented - a chore that often becomes repetitive in detail and lengthy. The ability to focus on a single topological space would, in many opinions, lead to deeper research and richer results. Surely the adaption of a proper single category for algebraic topology may lessen the rigor of analysizing ''the precise circumstances for which an argument works" yet simultaneously may keep a careful balance toward simplicity of the fundamentals of research and development in topology. There are many candidates among topological spaces for the focus of such studies; among these are those suggested in this paper whose constructions and characteristics are briefly outlined below to promote comparison and contrast among them.

Comments

An Essay submitted to the Faculty of the Graduate School, Marquette University, in Partial Fulfillment of the Requirement for the Degree of Master of Science, Milwaukee, Wisconsin

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