On the constructive notion of closure maps

Mathematical Logic Quarterly 58 (4-5):348-355 (2012)

Abstract
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 = A? In this paper, we study the notions of closed sets and closure maps in constructive reverse mathematics
Keywords closure maps  fan theorem.  Constructive reverse mathematics
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DOI 10.1002/malq.201110040
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An Interpretation of Intuitionistic Analysis.D. van Dalen - 1978 - Annals of Mathematical Logic 13 (1):1-43.
Constructive Notions of Equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
Glueing Continuous Functions Constructively.Douglas S. Bridges & Iris Loeb - 2010 - Archive for Mathematical Logic 49 (5):603-616.

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