Groups of homeomorphisms and normal subgroups of the group of permutations
In this paper, it is proved that no nontrivial proper normal subgroup of the group of permutations of a set X can be the group of homeomorphisms of (X,T) for any topology T on X.
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000650 |
| Summary: | In this paper, it is proved that no nontrivial proper normal subgroup of
the group of permutations of a set X can be the group of homeomorphisms of (X,T) for
any topology T on X. |
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| ISSN: | 0161-1712 1687-0425 |