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Continuity properties in constructive mathematics. (English) Zbl 0771.03018

The paper is devoted to the well-known problem of continuity in constructive mathematics. The presented approach is axiomatic. In particular, it is shown that every mapping of a complete separable space is continuous in constructive recursive mathematics and in intuitionism.

MSC:

03F60 Constructive and recursive analysis
46S30 Constructive functional analysis
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References:

[1] Constructive analysis (1985)
[2] Foundations of constructive analysis (1967) · Zbl 0183.01503
[3] The nonderivability in intuitionistic formal system of theorems on the continuity of effective operations 40 pp 321– (1983)
[4] Doklady Akademii Nauk SSSR 128 pp 49– (1959)
[5] Constructivism in mathematics 2 (1988)
[6] Constructivism in mathematics 1 (1988) · Zbl 0653.03040
[7] Nieuw Archief voor Wiskunde 15 pp 2– (1967)
[8] Church’s thesis without tears 48 pp 797– (1983) · Zbl 0527.03036
[9] DOI: 10.1002/malq.19880340202 · Zbl 0627.03044 · doi:10.1002/malq.19880340202
[10] Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR (LOMI) 20 pp 145– (1971)
[11] Lectures on constructive mathematical analysis (1985)
[12] Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences 245 pp 399– (1957)
[13] Continuity and nondiscontinuity in constructive mathematics 56 pp 1349– (1991)
[14] Varieties of constructive mathematics 97 (1987)
[15] Foundations of constructive mathematics (1985)
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