A metric characterization of zero-dimensional spaces
نویسندگان
چکیده
منابع مشابه
Perfect Images of Zero-dimensional Separable Metric Spaces
Let Q denote the rationals, P the irrationals, C the Cantor set and L the space C {p} (where p e C). Let / : X —> Y be a perfect continuous surjection. We show: (1) If X G { Q , P, QxP} , or if / is irreducible and Xe{C, L}, then Y is homeomorphic to X if Y is zero-dimensional. (2) If X G {P, C, L} and / is irreducible, then there is a dense subset S of Y such that / | /*~[S] is a homeomorphism...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1972-0288739-5