An embedding theorem for semigroups of continuous selfmaps (Q791672)
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scientific article; zbMATH DE number 3851387
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An embedding theorem for semigroups of continuous selfmaps |
scientific article; zbMATH DE number 3851387 |
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An embedding theorem for semigroups of continuous selfmaps (English)
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1983
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It is proved: If S(X) is the semigroup of all continuous selfmaps of the topological space X and X and Y are local dendrites with finite branch numbers then the following four statements are equivalent: (1) There exists a monomorphism from S(X) into S(Y) and also a monomorphism from S(Y) into S(X). (2) S(X) and S(Y) are isomorphic. (3) There exists a homeomorphism from X into Y and also a homeomorphism from Y into X. (4) X and Y are homeomorphic.
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local dendrites
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monomorphism
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homeomorphism
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