- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Isomorphisms between semigroups of maps
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Isomorphisms between semigroups of maps Warren, Eric
Abstract
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.
Item Metadata
Title |
Isomorphisms between semigroups of maps
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
1972
|
Description |
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.
|
Genre | |
Type | |
Language |
eng
|
Date Available |
2011-04-12
|
Provider |
Vancouver : University of British Columbia Library
|
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.
|
DOI |
10.14288/1.0080451
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Campus | |
Scholarly Level |
Graduate
|
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
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.