Doctoral Dissertations

Sahika Sahan

Abstract

"In this dissertation we investigate zero-dimensional compact metric spaces and their inverse limits. We construct an uncountable family of zero-dimensional compact metric spaces homeomorphic to their Cartesian squares. It is known that the inverse limit on [0,1] with an upper semi-continuous function with a connected graph has either one or infinitely many points. We show that this result cannot be generalized to the inverse limits on simple triods or simple closed curves. In addition to that, we introduce a class of zero-dimensional spaces that can be obtained as the inverse limits of arcs. We complete by answering a problem by Kelly and Meddaugh about the limits of inverse limits"--Abstract, page iv.

Advisor(s)

Charatonik, W. J.

Committee Member(s)

Roe, Robert Paul
Insall, Matt
Akin, Elvan
Nall, Van

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Summer 2017

Journal article titles appearing in thesis/dissertation

  • Zero-dimensional spaces homeomorphic to their Cartesian squares
  • Inverse limits with bonding functions whose graphs are arcs
  • Limits of inverse limits -- A counterexample

Pagination

viii, 42 pages

Note about bibliography

Includes bibliographic references.

Rights

© 2017 Sahika Sahan, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 11504

Electronic OCLC #

1104294562

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Included in

Mathematics Commons

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