Comparing spaces by means of 2-homeomorphismsстатья
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Дата последнего поиска статьи во внешних источниках: 10 августа 2018 г.
Аннотация:Topological spaces X and Y are called 2-homeomorphic if there exist homeomorphic closed subspaces of X and Y such that their complements are also homeomorphic. We give some sufficient conditions for spaces to be 2-homeomorphic. In particular, we show that if a space Y is conjugate to a space X, then X and Y are 2-homeomorphic. The complement R^n∖F of an arbitrary compact subset in the Euclidean space R^n is 2-homeomorphic to R^n. Some necessary conditions for two spaces to be 2-homeomorphic are also given. In particular, we capitalize on the next simple fact: if X and Y are nonempty 2-homeomorphic spaces, then some nonempty open subspaces U and V of X and Y, respectively, are homeomorphic.