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On the Recurrent Homeomorphisms of a Manifold
Author(s) -
Ho Chung-Wu
Publication year - 1977
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-16.3.541
Subject(s) - manifold (fluid mechanics) , topology (electrical circuits) , mathematics , space (punctuation) , boundary (topology) , topological space , open set , covering space , closed set , set (abstract data type) , pure mathematics , closed manifold , cover (algebra) , topological manifold , mathematical analysis , computer science , combinatorics , invariant manifold , functional analysis , mechanical engineering , biochemistry , chemistry , topological tensor product , engineering , gene , programming language , operating system
In a previous note, the author tried to estimate the “size” of the set of all the recurrent homeomorphisms of a given space and found that for a closed manifold X , with a non‐zero Euler characteristic, the set of the recurrent homeomorphisms is nowhere dense in the space of all the homeomorphisms of X under the compact open topology. He now extends the result to cover an arbitrary topological manifold with possibly a non‐empty boundary. Furthermore, the space of all the homeomorphisms of the space can be given either the compact open topology or the strong C 0 topology.