On the constructive notion of closure maps | Zendy

Ardeshir Mohammad | Zendy; Ramezanian Rasoul | Zendy

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On the constructive notion of closure maps

Author(s) -

Ardeshir Mohammad,

Ramezanian Rasoul

Publication year - 2012

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.201110040

Subject(s) - closure (psychology) , constructive , mathematics , constructive proof , set (abstract data type) , function (biology) , pure mathematics , calculus (dental) , discrete mathematics , algebra over a field , process (computing) , computer science , law , medicine , dentistry , evolutionary biology , political science , biology , programming language , operating system

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.

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