Topological Properties and Their Relations

Author

Suchitra Raman Sripada

Date of Graduation

Summer 2006

Degree

Master of Natural and Applied Science in Mathematics

Department

Mathematics

Committee Chair

Xingping Sun

Abstract

This research explores various properties of topological spaces, including compactness, Lindelöf, separability and countability. We emphasize the inter-relations among these properties. For example, we show that a compact space is Lindelöf, and that second countability implies the Lindelöf property and separability. For implications that are not true, we provide counter-examples. Metrizable topological spaces are called metric spaces, in which more properties may be studied. Boundedness, total boundedness, and completeness are such examples. Consequently, there are, in our opinion, more interesting inter-relations and implications we can discuss. As a highlight of this thesis, we show that, in metric space, compactness is equivalent to total boundedness and completeness. We also provide a counter-example that shows that boundedness and completeness do not imply compactness.

Keywords

compactness, second countability, Lindelöf, completeness, total boundedness

Subject Categories

Mathematics

Copyright

© Suchitra Raman Sripada

Recommended Citation

Sripada, Suchitra Raman, "Topological Properties and Their Relations" (2006). MSU Graduate Theses/Dissertations. 2732.
https://bearworks.missouristate.edu/theses/2732