Keywords

Convergence space, cauchy space, convergence semigroup, cauchy semigroup, continuous action, cauchy continuous action, compactification, completion, pseudoquotients

Abstract

Given a convergence space X, a continuous action of a convergence semigroup S on X and a compactification Y of X, under what conditions on X and the action on X is it possible to extend the action to a continuous action on Y . Similarly, given a Cauchy space X, a Cauchy continuous action of a Cauchy semigroup S on X and a completion Y of X, under what conditions on X and the action on X is it possible to extend the action to a Cauchy continuous action on Y . We answer the first question for some particular compactifications like the one-point compactification and the star compactification as well as for the class of regular compactifications. We answer the second question for the class of regular strict completions. Using these results, we give sufficient conditions under which the pseudoquotient of a compactification/completion of a space is the compactification/completion of the pseudoquotient of the given space

Notes

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Graduation Date

2013

Semester

Summer

Advisor

Richardson, Gary

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0004881

URL

http://purl.fcla.edu/fcla/etd/CFE0004881

Language

English

Release Date

August 2013

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Subjects

Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic

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Included in

Mathematics Commons

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