Discrete cells properties in the boundary set setting
Philip L. Bowers · Proceedings of the American Mathematical Society · 1985
Let X X be the complement of a σ − Z \sigma - Z -set in a locally compact separable ANR. It is proved that X X satisfies the discrete n n -cells property for each nonnegative integer n n if and only if X X satisfies the discrete approximation property. As a consequence, Hilbert space manifolds that arise as complements of boundary sets in Hilbert cube manifolds are characterized in terms of their homological structure coupled with a minimal amount of general positioning.