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- W2158817674 abstract "All topological spaces here are assumed to be T 2 . The collection F ( Y )of all homeomorphisms whose domains and ranges are closed subsets of a topological space Y is an inverse semigroup under the operation of composition. We are interested in the general problem of getting some information about the subsemigroups of F ( Y ) whenever Y is a compact metric space. Here, we specifically look at the problem of determining those spaces X with the property that F ( X ) is isomorphic to a subsemigroup of F ( Y ). The main result states that if X is any first countable space with an uncountable number of points, then the semigroup F ( X ) can be embedded into the semigroup F ( Y ) if and only if either X is compact and Y contains a copy of X , or X is noncompact and locally compact and Y contains a copy of the one-point compactification of X ." @default.
- W2158817674 created "2016-06-24" @default.
- W2158817674 creator A5088197950 @default.
- W2158817674 date "1977-07-01" @default.
- W2158817674 modified "2023-09-26" @default.
- W2158817674 title "Embedding inverse semigroups of homeomorphisms on closed subsets" @default.
- W2158817674 cites W2012315990 @default.
- W2158817674 doi "https://doi.org/10.1017/s0017089500003281" @default.
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