Local compactness and porosity in metric spaces
type: Item
instance of: scholarly article
title: Local compactness and porosity in metric spaces
zbMATH Open document ID: 0613.54016
author: S. J. Agronsky
author: Andrew M. Bruckner
published in: Real Analysis Exchange
publication date: 1986-01-01T00:00:00Z
review text: 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''.
Mathematics Subject Classification ID: 54E50
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 3992409
zbMATH Keywords: local compactness
zbMATH Keywords: porosity
zbMATH Keywords: metric spaces representable as convex subsets of separable Banach spaces
reviewed by: R. G. Woods
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3992409