Complexes with the disappearing closed set property
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- by Vyron M. Klassen PDF
- Proc. Amer. Math. Soc. 36 (1972), 583-585 Request permission
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.References
- P. H. Doyle and J. G. Hocking, A characterization of Euclidean $n$-space, Michigan Math. J. 7 (1960), 199–200. MR 121781
- P. H. Doyle and J. G. Hocking, Invertible spaces, Amer. Math. Monthly 68 (1961), 959–965. MR 131864, DOI 10.2307/2311802
- V. M. Klassen, The disappearing closed set property, Pacific J. Math. 43 (1972), 403–406. MR 319153
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 583-585
- MSC: Primary 57A15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0309118-8
- MathSciNet review: 0309118