On M-spaces and M*-spaces

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1970

Author dc:creator

• Nuckols, Thomas Ryland

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10919/76130

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/76130