×

Unsurprising results on localic groups. (English) Zbl 0718.18002

The central point of this paper is the following lemma on sublocales S, T of a localic group: \(S\cap T\) is nonzero if and only if \(e\in S^{-1}T\). The lemma is used in P. T. Johnstone’s simplified proof that localic subgroups are closed [Cah. Topologie Géom. Differ. Catégoriques 29, 157-161 (1988; Zbl 0648.18007)], and Johnstone has generalized it for further application.

MSC:

18B25 Topoi

Citations:

Zbl 0648.18007
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Isbell, J.; Kr̆íz̆, I.; Pultr, A.; Rosícky, J., Remarks on Localic Groups (1986), Preprint · Zbl 0661.22003
[2] Johnstone, P. T., Stone Spaces (1982), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0499.54001
[3] Joyal, A.; Tierney, M., An extension of the Galois theory of Grothendieck, Mem. Amer. Math. Soc., 309 (1984) · Zbl 0541.18002
[4] Waterhouse, W. C., Introduction to Affine Group Schemes (1979), Springer: Springer Berlin · Zbl 0442.14017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.