Local compactness and porosity in metric spaces
The authors generalize the concept of porosity, previously studied only for the real line, to all metric spaces. They then study this generalization in detail for metric spaces representable as convex subsets of separable Banach spaces, and obtain theorems such as the following: Let A be a convex subset of a separable Banach space with \(| A| >1\). The following are equivalent: (1) A has a non-porous compact subset. (2) A has a nowhere dense compact subset that is not a countable union of porous sets. (3) A is locally compact. Further, if A is not locally compact then every compact subset of X is ''totally porous''.
metric spaces representable as convex subsets of separable Banach spaces
scientific article; zbMATH DE number 3992409