Open Access
2016 Essential Closures
Pongpol Ruankong, Songkiat Sumetkijakan
Real Anal. Exchange 41(1): 55-86 (2016).


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. A typical essential closure collects all points which 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.


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Pongpol Ruankong. Songkiat Sumetkijakan. "Essential Closures." Real Anal. Exchange 41 (1) 55 - 86, 2016.


Published: 2016
First available in Project Euclid: 29 March 2017

zbMATH: 1316.62065
MathSciNet: MR3511936

Primary: 28A20 , 28A35
Secondary: 46B20 , 60A10 , 60B10

Keywords: essential closures , lower density operators , non-essential sets , stochastic closures , submeasures , topological closures

Rights: Copyright © 2016 Michigan State University Press

Vol.41 • No. 1 • 2016
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