In this thesis we investigate the properties of M-spaces and M*-spaces, which are generalized metric spaces. Chapter II is devoted to preliminary results, and in Chapter III we prove the characterization for M-spaces theorem of K. Morita [12]. This theorem states that a space X is an M-space if and only if there exists a quasi-perfect map from X onto a metrizable space T.
Chapter IV is concerned with the relationships between M-spaces and M*-spaces. We first prove an M-space is an expandable, M*'-space and then show that every normal, expandable, M*-space is an M-space. Using Katetov's Theorem, we show that in a collectionwise normal space, X is an M-space if and only if it is an M*-space. We conclude by generalizing this to the following. In a normal space X, X is an M-space if and only if it is an M*-space.
Chapter V is concerned with the study of M-spaces and M*-spaces under quasi-perfect maps. We also prove the Closed Subspace Theorem for M-spaces and M*-spaces and establish the Locally Finite Sum Theorem for M-spaces and M*-spaces.
In Chapter VI, we give an example of a T₂, locally compact M-space X, which is not normal and therefore not metrizable. We also give an example of a T₂, locally compact M*-space Y, which is not an M-space, but is however the image of X under a quasi-perfect mapping. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/76130 |
| Date | January 1970 |
| Creators | Nuckols, Thomas Ryland |
| Contributors | Mathematics |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | iv, 49 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 33887015 |
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