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ESSENTIAL CLOSURES.
- Source :
-
Real Analysis Exchange . 2016, Vol. 41 Issue 1, p55-85. 31p. - Publication Year :
- 2016
-
Abstract
- Based on the Zermelo-Fraenkel system of axioms ZF, we introduce a theory of essential closures. It is a generalization of the concept of topological closures in which a set may not be contained in its essential closure. A typical essential closure collects all points that are essential with respect to a submeasure; hence it is called a submeasure closure. One of our main results states that a "nice" essential closure must be a submeasure closure. Many examples of known and new submeasure closures are discussed and their applications are demonstrated, especially in the study of the supports of measures. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01471937
- Volume :
- 41
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Real Analysis Exchange
- Publication Type :
- Academic Journal
- Accession number :
- 119508857
- Full Text :
- https://doi.org/10.14321/realanalexch.41.1.0055