# A categorical account of the localic closed subgroup theorem

Commentationes Mathematicae Universitatis Carolinae (2007)

- Volume: 48, Issue: 3, page 541-553
- ISSN: 0010-2628

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topTownsend, Christopher. "A categorical account of the localic closed subgroup theorem." Commentationes Mathematicae Universitatis Carolinae 48.3 (2007): 541-553. <http://eudml.org/doc/250198>.

@article{Townsend2007,

abstract = {Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.},

author = {Townsend, Christopher},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {locale; power locale; Hofmann-Mislove theorem; closed subgroup; compact locale; fitted sublocale; categorical logic; category of locales; group; subspace; open object; closed subset},

language = {eng},

number = {3},

pages = {541-553},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A categorical account of the localic closed subgroup theorem},

url = {http://eudml.org/doc/250198},

volume = {48},

year = {2007},

}

TY - JOUR

AU - Townsend, Christopher

TI - A categorical account of the localic closed subgroup theorem

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2007

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 48

IS - 3

SP - 541

EP - 553

AB - Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.

LA - eng

KW - locale; power locale; Hofmann-Mislove theorem; closed subgroup; compact locale; fitted sublocale; categorical logic; category of locales; group; subspace; open object; closed subset

UR - http://eudml.org/doc/250198

ER -

## References

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