Loewner differential equation - Revision history

en>Quondum: replacing redirect Holomorphic to dab page with appropriate destination Holomorphic function

2014-12-08T01:50:21Z

replacing redirect Holomorphic to dab page with appropriate destination Holomorphic function

en>Enyokoyama: /* Loewner chain */ add the link to "uniformly continuous"

2014-02-04T10:30:19Z

Loewner chain: add the link to "uniformly continuous"

← Older revision		Revision as of 12:30, 4 February 2014
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	~~In [[mathematics]]~~, a ~~[[topological space]]~~ ''~~X'' is said~~ to ~~be '''H-closed'''~~, ~~or '''Hausdorff closed''~~', ~~or ''~~'~~absolutely closed''' if it is closed~~ in ~~every [[Hausdorff space]] space containing~~ it ~~as a subspace~~. ~~This property is~~ a ~~generalization of~~ [~~[compact spaces\|compactness]], since a compact subset of a Hausdorff space is closed~~. ~~Thus, every compact Hausdorff space is H~~-~~closed~~. ~~The notion of an H-closed space has been introduced in 1924 by [[Pavel Alexandrov\|P~~. ~~Alexandroff]] and [[Pavel Samuilovich Urysohn\|P~~. ~~Urysohn]~~].		THE HAIR<br>Rebecca Gonsalves: The higher the hair, the closer to God is not a tenet you'd expect Ms Margulies to live by, but it's all the better to show off those wonderful eyebrows.<br><br>Hugh Montgomery: We personally liked the Nurse Hathaway curls but hey, even as we hum TLC's "Waterfalls", we appreciate you can't live in 1995 forever.<br>THE SUIT<br>Rebecca: Kinda naff, but the fact it's accessorised with the happiest smile ever makes my Grinch-y fashion heart grow three sizes.<br><br>Hugh: Surely everyone knows that if you wear a white tux, you need to wear it backwards, [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine] Dion-style, or be found wanting.<br>THE BAG<br>Rebecca: Not exactly an earth-shattering choice, but perfect for accentuating her dance moves should she come over with a case of 'Saturday Night Fever'. <br>Hugh: The kind of uselessly prosaic accessory that makes us lose faith in this vocation of ours.<br>THE [http://www.dailymail.co.uk/home/search.html?sel=site&searchPhrase=JEWELLERY JEWELLERY]<br>Rebecca: Chandelier earrings are a surprisingly romantic choice that are steered into 'maid of honour' territory by such a plump bun. <br><br>Hugh: From 'Good Wife' to Pat Butcher? No. Too obvious. They're great.

	~~==Examples and equivalent formulations==~~

	* The unit interval <~~math~~>~~[0,1]~~<~~/math~~>, ~~endowed~~ with ~~the smallest topology which refines the euclidean topology, and contains~~ <~~math~~>~~Q \cap~~ [~~0,1]<~~/~~math> as an open set is H-closed but not compact~~.

	* Every [[regular space\|regular]] Hausdorff H-closed space is compact.

	* A Hausdorff space is H-closed if and only if every open cover has a finite subfamily with dense union.

	==~~See also~~==

	*[[Compact space]]

	~~==References==~~

	* K.P. Hart, Jun-iti Nagata, J.E. Vaughan (editors), ''~~Encyclopedia~~ of ~~General Topology~~'~~', Chapter d20 (~~by ~~Jack Porter and Johannes Vermeer)~~


	~~[[Category~~:~~Properties of topological spaces]]~~
	~~[[Category:Compactness (mathematics)]]~~

en>Rjwilmsi: /* References */Journal cites, added 1 DOI using AWB (9888)

2014-01-26T08:25:06Z

References: Journal cites, added 1 DOI using AWB (9888)

← Older revision		Revision as of 10:25, 26 January 2014
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	~~Nothing~~ to ~~write about me really~~.~~<br>Feels good to be~~ a ~~member~~ of ~~wmflabs~~.~~org~~.<br>~~I really wish I'm useful at all~~<br><br>~~Also visit my site ::~~ [~~http:~~/~~/wattsbuilding~~.~~com/sale/uggs~~.~~asp uggs sale boots~~]		In [[mathematics]], a [[topological space]] ''X'' is said to be '''H-closed''', or '''Hausdorff closed''', or '''absolutely closed''' if it is closed in every [[Hausdorff space]] space containing it as a subspace. This property is a generalization of [[compact spaces\|compactness]], since a compact subset of a Hausdorff space is closed. Thus, every compact Hausdorff space is H-closed. The notion of an H-closed space has been introduced in 1924 by [[Pavel Alexandrov\|P. Alexandroff]] and [[Pavel Samuilovich Urysohn\|P. Urysohn]].

			==Examples and equivalent formulations==

			* The unit interval <math>[0,1]</math>, endowed with the smallest topology which refines the euclidean topology, and contains <math>Q \cap [0,1]</math> as an open set is H-closed but not compact.

			* Every [[regular space\|regular]] Hausdorff H-closed space is compact.

			* A Hausdorff space is H-closed if and only if every open cover has a finite subfamily with dense union.

			==See also==

			*[[Compact space]]

			==References==

			* K.P. Hart, Jun-iti Nagata, J.E. Vaughan (editors), ''Encyclopedia of General Topology'', Chapter d20 (by Jack Porter and Johannes Vermeer)


			[[Category:Properties of topological spaces]]
			[[Category:Compactness (mathematics)]]

en>GoingBatty: Typo fixing, general fixes & manual clean up using AWB (7910)

2012-01-11T03:14:57Z

Typo fixing, general fixes & manual clean up using AWB (7910)

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