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- W1992845785 abstract "Let H(C) be the group of homeomorphisms of the Cantor set, C , onto itself. Let p: C → M be a map of C onto a compact metric space M , and let G(p, M) be is a group. The map p: C → M is standard , if for each (x, y) ∈ C × C such that p(x) = p(y) , there is a sequence and a sequence such that x n → x and h n ( x n ) → y Standard maps and their associated groups characterize compact metric spaces in the sense that: Two such spaces, M and N , are homeomorphic if and only if, given p standard from C onto M , there is a standard q from C onto N for which G(p, M) = h −1 G(q, N)h , for some h ∈ H(C) The present paper exhibits a structure theorem connecting these characterizing subgroups of H(C) and products of spaces: Let M 1 and M 2 be compact metric spaces. Then there are standard maps p: C → M 1 × M 2 and p i : C → M i , i = 1, 2, such that G(p, M 1 × M 2 ) = G(p 1 , M 1 ) ∩ G(p 2 , M 2 ) ." @default.
- W1992845785 created "2016-06-24" @default.
- W1992845785 creator A5016960686 @default.
- W1992845785 date "1969-04-01" @default.
- W1992845785 modified "2023-09-27" @default.
- W1992845785 title "A theorem on homeomorphism groups and products of spaces" @default.
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- W1992845785 doi "https://doi.org/10.1017/s0004972700041344" @default.
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