A topological space may be viewed as an algebraic structure.
For example, it may be viewed as a (complete atomic) Boolean algebra equipped with a closure operator. The lattice of closed subsets is another algebraic structure which may be associated with a topological space. Tne purpose of this thesis is primarily to investigate the metamathematical properties of algebraic structures associated with topological spaces.
More specifically, we will first consider questions of decidability
of the theories of these algebraic structures. It turns out that these theories are undecidable. We will also examine certain
equivalence relations on the class of topological spaces that arise naturally from viewing them as first-order structures. Finally
we will show that certain classical theorems of model theory do not hold for topological spaces. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/18788 |
| Date | January 1974 |
| Creators | Inglis, John Malyon |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| 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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