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A characterization of the uniform closure of the set of homeomorphisms of a compact totally disconnected metric space into itself
1982
Proceedings of the American Mathematical Society
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The limit index X(x) of a point x in a compact metric space is defined. (Roughly: Isolated points have index 0, limit points have index 1, limit points of limit points have index 2, and so forth.) Then the following theorem is proved. Theorem 1. Let E be a compact, totally disconnected metric space. Then the uniform closure of the set of homeomorphisms of E into itself is the set C^ of continuous functions ¡from E to E satisfying
doi:10.1090/s0002-9939-1982-0637180-8
fatcat:kflxl6vvufezbj4p5hangnlpdy