Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T04:43:13.266Z Has data issue: false hasContentIssue false

A proof–technique in uniform space theory

Published online by Cambridge University Press:  12 March 2014

Douglas Bridges
Affiliation:
Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand, E-mail: [email protected]
Luminiţa Vîţă
Affiliation:
Department of Mathematics & Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand, E-mail: [email protected]

Abstract

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Beeson, M. J., Foundations of constructive mathematics, Springer-Verlag, Heidelberg, 1985.Google Scholar
[2] Bishop, E. and Bridges, D. S., Constructive analysis, Grundlehren der mathematischen Wissenschaften, vol. 279, Springer–Verlag, Heidelberg, 1985.Google Scholar
[3] Bourbaki, N., General topology (Part 1), Addison–Wesley, Reading, MA, 1966.Google Scholar
[4] Bridges, D. S., Ishihara, H., Schuster, P. M., and Vîţă, L. S., Strong continuity implies uniform sequential continuity, preprint, Ludwig–Maximilians Universität, München, 2001.Google Scholar
[5] Bridges, D. S. and Richman, F., Varieties of constructive mathematics, London Mathematical Society Lecture Notes, no. 95, Cambridge University Press, London, 1987.Google Scholar
[6] Bridges, D. S., Richman, F., and Schuster, P. M., A weak countable choice principle, Proceedings of the American Mathematical Society, vol. 128 (2000), no. 9, p. 27492752.CrossRefGoogle Scholar
[7] Bridges, D. S. and Vîţă, L. S., Strong continuity and uniform continuity: the uniform space case, preprint, University of Canterbury, Christchurch, New Zealand, 2001.Google Scholar
[8] Bridges, D. S. and Vîţă, L. S., Apartness spaces as a framework for constructive topology, Annals of Pure and Applied Logic, vol. 119 (2002), no. 1–3, p. 6183.Google Scholar
[9] Schuster, P. M., Bridges, D. S., and Vîţă, L. S., Apartness as a relation between subsets, Combinatorics, computability and logic (Calude, C. S., Dinneen, M. J., and Sburlan, S., editors), Proceedings of DMTCS'01, Constanţa, Romania, 2–6 07 2001, DMTCS Series, vol. 17, Springer–Verlag, London, 2001, p. 203214.Google Scholar
[10] Troelstra, A. S. and van Dalen, D., Constructivism in mathematics, vol. I, II, North–Holland Publ. Co., Amsterdam, 1988.Google Scholar
[11] Vîţă, L. S. Proximal and uniform convergence, Mathematical Logic Quarterly, vol. 3 (2003), p. 255259.Google Scholar