An Alternative Description of Approach Spaces Via Approach Cores
| Autor: | Mark Sioen, W. Van Den Haute |
|---|---|
| Přispěvatelé: | Mathematics, Topological Algebra, Functional Analysis and Category Theory, Faculty of Sciences and Bioengineering Sciences |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
General Computer Science
01 natural sciences Interior operator Upper regular function frame Theoretical Computer Science Approach space Hull Closure operator Point (geometry) 0101 mathematics Mathematics Discrete mathematics Approach core Algebra and Number Theory Degree (graph theory) 010102 general mathematics Function (mathematics) Closure tower Lower hull operator 010101 applied mathematics Lower regular function frame Interior tower Theory of computation Upper hull operator closure operator Interior point method |
| Popis: | The aim of this note is, following a suggestion from Lowen (2015), to give an isomorphic description of the topological construct App of approach spaces by means of families of [0, ∞]-valued functionals, which we will call approach cores, collectively measuring ‘to which degree a point can be considered to be an interior point of a subset’. We will also investigate the relation between these approach cores and other alternative descriptions of approach spaces such as a.o. via the upper hull and upper regular function frame, and from this derive a result on initiality in App of a source derived from the upper hull, which is a counterpart to a result from Lowen (2015) only available for the lower hull up till now. |
| Databáze: | OpenAIRE |
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