On the constructive notion of closure maps

On the constructive notion of closure maps

Let A be a subset of the constructive real line. What are the necessary and sufficient conditions for the set A such that A is continuously separated from other reals, i.e., there exists a continuous function f with f−1(0) = A? In this paper, we study the notions of closed sets and closure maps in c...

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Veröffentlicht in:Mathematical logic quarterly 2012-08, Vol.58 (4-5), p.348-355
Hauptverfasser: Ardeshir, Mohammad, Ramezanian, Rasoul
Format: Artikel
Sprache:eng
Schlagworte:
closure maps
Constructive reverse mathematics
fan theorem
Studies
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Zusammenfassung:Let A be a subset of the constructive real line. What are the necessary and sufficient conditions for the set A such that A is continuously separated from other reals, i.e., there exists a continuous function f with f−1(0) = A? In this paper, we study the notions of closed sets and closure maps in constructive reverse mathematics.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.201110040