Journal of Symbolic Logic

A proof—technique in uniform space theory

Douglas Bridges and Luminiţa Vîţă

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In the constructive theory of uniform spaces there occurs a technique of proof in which the application of a weak form of the law of excluded middle is circumvented by purely analytic means. The essence of this proof—technique is extracted and then applied in several different situations.

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J. Symbolic Logic Volume 68, Issue 3 (2003), 795- 802.

First available in Project Euclid: 17 July 2003

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Zentralblatt MATH identifier

Primary: 03B60: Other nonclassical logic 03F60: Constructive and recursive analysis [See also 03B30, 03D45, 03D78, 26E40, 46S30, 47S30]


Bridges, Douglas; Vîţă, Luminiţa. A proof—technique in uniform space theory. J. Symbolic Logic 68 (2003), no. 3, 795-- 802. doi:10.2178/jsl/1058448439.

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  • M. J. Beeson Foundations of constructive mathematics, Springer-Verlag, Heidelberg,1985.
  • E. Bishop and D. S. Bridges Constructive analysis, Grundlehren der mathematischen Wissenschaften, vol. 279, Springer\textendash Verlag, Heidelberg,1985.
  • N. Bourbaki General topology (Part 1), Addison\textendash Wesley, Reading, MA,1966.
  • D. S. Bridges, H. Ishihara, P. M. Schuster, and L. S. Vîţă Strong continuity implies uniform sequential continuity, preprint, Ludwig\textendash Maximilians Universität, München,2001.
  • D. S. Bridges and F. Richman Varieties of constructive mathematics, London Mathematical Society Lecture Notes, no. 95, Cambridge University Press, London,1987.
  • D. S. Bridges, F. Richman, and P. M. Schuster A weak countable choice principle, Proceedings of the American Mathematical Society, vol. 128 (2000), no. 9, p. 2749\textendash2752.
  • D. S. Bridges and L. S. Vîţă Strong continuity and uniform continuity: the uniform space case, preprint, University of Canterbury, Christchurch, New Zealand,2001.
  • P. M. Schuster, D. S. Bridges, and L. S. Vîţă Apartness as a relation between subsets, Combinatorics, computability and logic (C. S. Calude, M. J. Dinneen, and S. Sburlan, editors), Proceedings of DMTCS'01, Constanţa, Romania, 2\textendash6 July 2001, DMTCS Series, vol. 17, Springer\textendash Verlag, London,2001, p. 203\textendash214.
  • A. S. Troelstra and D. van Dalen Constructivism in mathematics, vol. I, II, North\textendash Holland Publ. Co., Amsterdam,1988.
  • L. S. Vîţă Proximal and uniform convergence, Mathematical Logic Quarterly, vol. 3 (2003), p. 255\textendash259.