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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(0) = A? In this paper, we study the notions of closed sets and closure maps in constructive reverse mathematics.Other Versions
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References found in this work
An interpretation of intuitionistic analysis.D. van Dalen - 1978 - Annals of Mathematical Logic 13 (1):1.
Sequences of real functions on [0, 1] in constructive reverse mathematics.Hannes Diener & Iris Loeb - 2009 - Annals of Pure and Applied Logic 157 (1):50-61.
Constructive notions of equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
The anti-Specker property, a Heine–Borel property, and uniform continuity.Josef Berger & Douglas Bridges - 2008 - Archive for Mathematical Logic 46 (7-8):583-592.
Decidability and Specker sequences in intuitionistic mathematics.Mohammad Ardeshir & Rasoul Ramezanian - 2009 - Mathematical Logic Quarterly 55 (6):637-648.
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