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Separation axioms and minimal topologies Liaw, Saw-Ker
Abstract
A hierarchy of separation axioms can be obtained by considering which axiom implies another. This thesis studies the properties of some separation axioms between T₀ and T₁ and investigates where each of the axioms belongs in this hierarchy. The behaviours of the axioms under strengthenings of topologies and cartesian products are considered.
Given a set X, the family of all topologies defined on X is a complete lattice. A study of topologies which are minimal in this lattice with respect to a certain separation axiom is made. We consider certain such minimal spaces, obtain some characterizations and study some of their properties.
Item Metadata
| Title |
Separation axioms and minimal topologies
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
1971
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| Description |
A hierarchy of separation axioms can be obtained by considering which axiom implies another. This thesis studies the properties of some separation axioms between T₀ and T₁ and investigates where each of the axioms belongs in this hierarchy. The behaviours of the axioms under strengthenings of topologies and cartesian products are considered.
Given a set X, the family of all topologies defined on X is a complete lattice. A study of topologies which are minimal in this lattice with respect to a certain separation axiom is made. We consider certain such minimal spaces, obtain some characterizations and study some of their properties.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2011-05-10
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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| DOI |
10.14288/1.0080463
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| URI | |
| Degree (Theses) | |
| Program (Theses) | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.