Spaces admitting topologically transitive maps by Anima Nagar and V. Kannan

Topology Proceedings 26 No. 1 (2001-2002), pp. 297-306

Spaces admitting topologically transitive maps

Anima Nagar and V. Kannan

In this paper, after observing that on certain topological spaces there are no topologically transitive maps at all, we characterize all those locally compact subspaces of the real line that admit a topologically transitive map. We prove that any locally compact subspace X of R admitting a topologically transitive map, must be one of the following up to homeomorphism: (1) Finite discrete space; (2) Finite union of nontrivial compact intervals; (3) Finite union of nontrivial noncompact intervals; (4) Cantor set K; (5) K + N.

Keywords: Cantor set, locally compact, topologically transitive
Mathematics Subject Classification: 54H20

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Topology Proceedings, Volume 26 No. 1 (2001-2002)
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