Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T04:56:46.795Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak compactness in constructive spaces

Published online by Cambridge University Press:  24 October 2008

J. J. C. Vermeulen
J. J. C. Vermeulen
Affiliation:
Department of Mathematics, University of Cape Town, Rondebosch 7700, South Africa
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce a constructively weak variant of compactness for locales as a supplement to weak closure, a notion which has featured in the constructive formulation of some recent results in locale theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 1 , January 1992 , pp. 63 - 74
Copyright
Copyright © Cambridge Philosophical Society 1992

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

1Isbell, J. R., Keiz, I., Pultr, A. and Rozicky, J.. Remarks on localic groups. In Categorical Algebra and its Applications (Louvain-La-Neuve, 1987), Lecture Notes in Math. vol. 1348 (Springer-Verlag, 1988), pp. 154172.Google Scholar
2Johnstone, P. T.. Topos Theory. London Math. Soc. Mathematical Monographs no. 10 (Academic Press. 1977).Google Scholar
3Johnstone, P. T.. Stone Spaces. Cambridge Studies in Advanced Math. no. 3 (Cambridge University Press, 1982).Google Scholar
4Johnstone, P. T.. A constructive closed subgroup theorem for localic groups and groupoids. Cahiers Topologie Gom. Diffrentielle Catgorigues 30 (1989), 323.Google Scholar
5Joyal, A. and Tierney, M.. An Extension of the Galois Theory of Grothendieck. Memoirs Amer. Math. Soc. no. 309 (American Mathematical Society, 1984).CrossRefGoogle Scholar
6Kock, A., Lecouturier, P. and Mikkelsen, C. J.. Some topos-theoretic concepts of finiteness. In Model Theory and Topoi, Lecture Notes in Math. vol. 445 (Springer-Verlag, 1975), pp. 209283.CrossRefGoogle Scholar
7Scott, D. S.. Identity and existence in intuitionistic logic. In Applications of Sheaves, Lecture Notes in Math. vol. 753 (Springer-Verlag, 1979), pp. 660696.Google Scholar
8Vermeulen, J. J. C.. A note on iterative arguments in a topos. Math. Proc. Cambridge Philos. Soc. 110 (1991), 5762.Google Scholar