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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Complexes with the disappearing closed set property


Author: Vyron M. Klassen
Journal: Proc. Amer. Math. Soc. 36 (1972), 583-585
MSC: Primary 57A15
MathSciNet review: 0309118
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Abstract: A topological space X is said to have the disappearing closed set (DCS) property if and only if for every proper closed subset C there is a sequence of homeomorphisms $ \{ {h_i}\} ,i = 1,2,3, \cdots ,$, of X onto X, and a decreasing sequence of open subsets $ \{ {U_i}\} ,i = 1,2,3, \cdots $ , of X such that $ \cap _{i = 1}^\infty {U_i} = \emptyset $ and $ {h_i}(C) \subseteq {U_i}$. Theorem. A finite simplicial n-complex is an n-manifold if and only if it has the DCS property.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0309118-8
PII: S 0002-9939(1972)0309118-8
Keywords: n-manifold, n-complex, disappearing closed set property
Article copyright: © Copyright 1972 American Mathematical Society