Let X and Y be topological spaces and C and D semigroups under composition of maps from X to X and Y to Y respectively. Let H be an isomorphism from C to D; it is shown that if both C and D contain the constant maps then there exists a bijection h from X to Y such that H(f) = h∘f∘h⁻¹, VfɛC. We investigate this situation and find sufficient conditions for this h to be a homeomorphism. In this regard we study the familiar semigroups of continuous, closed, and connected maps.
An auxiliary problem is the case when C = D and H is an automorphism of D), We then ask when is every automorphism is inner. The question is answered for certain particular semigroups; e.g., the semigroup of differentiable maps on the reals has the property that all automorphisms are inner. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/33545 |
| Date | January 1972 |
| Creators | Warren, Eric |
| Publisher | University of British Columbia |
| 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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