Relatively compact subset - Revision history

Vipul: 3 revisions

2008-05-11T19:57:54Z

3 revisions

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Vipul at 16:42, 22 January 2008

2008-01-22T16:42:36Z

← Older revision		Revision as of 16:42, 22 January 2008
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	A subset of a [[topological space]] is termed '''relatively compact''' if its [[closure]] in the space is [[compact space\|compact]].		A subset of a [[topological space]] is termed '''relatively compact''' if its [[closure]] in the space is [[compact space\|compact]].

	Note that when the space is a [[Hausdorff space]], or more generally, a [[KC-space]], it suffices to say that the ~~open~~ subset is contained in a compact subset.		Note that when the space is a [[Hausdorff space]], or more generally, a [[KC-space]], it suffices to say that the subset is contained in a compact subset.
			(The equivalence of definitions relies on the fact that [[compactness is weakly hereditary\|a closed subset of a compact space is compact]] and [[Hausdorff implies KC\|a compact subset of a Hausdorff space is closed]]).

Vipul at 16:41, 22 January 2008

2008-01-22T16:41:23Z

← Older revision		Revision as of 16:41, 22 January 2008
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	A subset of a [[topological space]] is termed '''relatively compact''' if its [[closure]] in the space is [[compact space\|compact]].		A subset of a [[topological space]] is termed '''relatively compact''' if its [[closure]] in the space is [[compact space\|compact]].

			Note that when the space is a [[Hausdorff space]], or more generally, a [[KC-space]], it suffices to say that the open subset is contained in a compact subset.

Vipul at 08:45, 18 August 2007

2007-08-18T08:45:08Z

New page

{{toposubspace property}}

==Definition==

A subset of a [[topological space]] is termed '''relatively compact''' if its [[closure]] in the space is [[compact space|compact]].