Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658082 | Topology and its Applications | 2016 | 17 Pages |
Abstract
The first author introduced a measure of compactness for families of sets, relative to a class of filters, in the context of convergence approach spaces. We characterize a variety of maps (types of quotient maps, closed maps, and variants of perfect maps) as those respecting this measure of compactness under one form or another. We establish a product theorem for measure of compactness that yields as instances new product theorems for spaces and maps, and new product characterizations of spaces and maps, thus extending existing results from the category of convergence spaces to that of convergence approach spaces. In particular, results of the Mròwka-Kuratowski type are obtained, shedding new light on existing results for approach spaces.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Frédéric Mynard, William Trott,