dc.contributor.advisor Hamilton, Olan H. dc.contributor.author Aslan, Farhad en_US dc.date.accessioned 2019-10-11T15:11:01Z dc.date.available 2019-10-11T15:11:01Z dc.date.created 1969 en_US dc.date.issued 1969 en_US dc.identifier aleph-234940 en_US dc.identifier.uri https://repository.tcu.edu/handle/116099117/33801 dc.description.abstract In 1965, M. Wiscamb [30] studied two classes of generalized metric spaces called A1 and A2 spaces. She showed that Ai -spaces i = 1, 2 include the class of metrizable spaces and are contained in the class of collectionwise normal spaces. The purpose of this paper is to study these spaces, their properties, and introduce other intermediate spaces between A1 -spaces and the class of collectionwise normal spaces. Three classes of generalized metric spaces, A0 , 2-fold-fully normal, and almost-2-fold fully normal spaces are defined and their properties are studied. It is shown that an A0-space is completely normal and that the class of Ai-spaces possess all the properties of the class of-A0 -spaces. Some of the results are shown in the following implication diagram: " J. Ceder in [3] conjectured that a paracompact semi-metric space is an M3-space. However, this conjecture is false as R. W. Heath in [8] gave an example of a paracompact semi-metric space which is not an M3-space. It remains unknown, then, what condition on a semi-metric space gives an M3-space. Interesting enough, it is shown that every semi-metrizable Ai-space, i = 0, 1, 2 is an M3-space (Theorem 5.6). Finally, some properties of semi-metrizable Ai-spaces i = 0, 1, 2 are discussed and necessary and sufficient conditions for metrizability of Ai-spaces, i= 0, 1, 2 are given. dc.format.extent iii, 41 leaves, bound en_US dc.format.medium Format: Print en_US dc.language.iso eng en_US dc.relation.ispartof Texas Christian University dissertation en_US dc.relation.ispartof AS38.A85 en_US dc.subject.lcsh Metric spaces en_US dc.title Some generalizations of metric spaces en_US dc.type Text en_US etd.degree.department Department of Mathematics etd.degree.level Doctoral local.college College of Science and Engineering local.department Mathematics local.academicunit Department of Mathematics dc.type.genre Dissertation local.subjectarea Mathematics dc.identifier.callnumber Main Stacks: AS38 .A85 (Regular Loan) dc.identifier.callnumber Special Collections: AS38 .A85 (Non-Circulating) etd.degree.name Doctor of Philosophy etd.degree.grantor Texas Christian University
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