Measure of compactness for filters in product spaces: Kuratowski–Mròwka in CAP revisited
| Autor: | Frédéric Mynard, William Trott |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Topological tensor product 010102 general mathematics Discontinuous linear map 01 natural sciences Perfect map 010101 applied mathematics Approach space 54A05 54A20 54B10 54B30 54C10 54C60 54D20 54D30 Product measure Compact-open topology Interpolation space Geometry and Topology 0101 mathematics Modes of convergence Mathematics - General Topology Mathematics |
| Zdroj: | Topology and its Applications. 200:251-267 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2015.06.013 |
| Popis: | 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 Mrowka–Kuratowski type are obtained, shedding new light on existing results for approach spaces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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