Complexes with the disappearing closed set property

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.