Title

Separation properties in topological categories

Date of Award

1990

Availability

Article

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics

First Committee Member

Marvin Mielke, Committee Chair

Abstract

This paper is concerned with a study of certain generalizations to arbitrary topological categories of the separation properties $T\sb{0},T\sb{1},T\sb{2},T\sb{3}$, and $T\sb{4}$ for topological spaces. These generalizations include two notions of $T\sb{0}$, one notion of $T\sb{1}$, and four notions of each $T\sb{2},T\sb{3}$, and $T\sb4$. It is shown that each of these notions reduces to the corresponding classical notion in the case of topological spaces. General results involving relationships among thee various generalized separation properties as well as interrelationships among their various forms are established. Moreover, an explicit characterization of each of these separation properties is given in approximately twenty five topological categories of wide interest.

Keywords

Mathematics

Link to Full Text

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