| In this paper we present the homeomorphism groups of manifolds, explaining why non-metrizable manifolds are better behaved, with regard to their homeomorphism groups, than metrizable manifolds. A proof that the natural topology on the homeomorphism group for a one dimensional metrizable manifold is the minimum group topology but the homeomorphism group does not admit a minimum group topology for a more than one dimensional metrizable manifold will be given. Likewise, examples demonstrating how badly behaved are the homeomorphism groups of continua, in comparison with homeomorphism groups of manifolds is also given. |
Keywords
homeomorphism group; non-metrizable manifold; Cook's curve; continua; minimum group topology.
Math Review Classification
Primary AMS (1991) Subject Classification: 54E30, 54E35
Last Updated
8 September 1999
Length
11 pages
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