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