Proper map - Revision history

Vipul: 7 revisions

2008-05-11T19:57:41Z

7 revisions

← Older revision	Revision as of 19:57, 11 May 2008
(No difference)

Vipul: /* Definition */

2008-01-13T17:09:41Z

Definition

← Older revision		Revision as of 17:09, 13 January 2008
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	===Symbol-free definition===		===Symbol-free definition===

	A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if it is [[closed map\|closed]] the inverse image of any [[compact space\|compact subset]] in the image set, is a compact subset of the domain. Equivalently, it is a [[closed map]] and the inverse image of any point is a compact subset of the domain.		A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if it is [[closed map\|closed]] and the inverse image of any [[compact space\|compact subset]] in the image set, is a compact subset of the domain. Equivalently, it is a [[closed map]] and the inverse image of any point is a compact subset of the domain.

	==Relation with other properties==		==Relation with other properties==

Vipul at 01:33, 27 October 2007

2007-10-27T01:33:36Z

@@ Line 1: / Line 1: @@
-{{topospace property}}
+{{continuous map property}}
 ==Definition==
@@ Line 5: / Line 5: @@
 ===Symbol-free definition===
-A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if it is [[closed map|closed]] the inverse image of any [[compact space|compact subset]] in the image set, is a compact subset of the domain.
+A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if it is [[closed map|closed]] the inverse image of any [[compact space|compact subset]] in the image set, is a compact subset of the domain. Equivalently, it is a [[closed map]] and the inverse image of any point is a compact subset of the domain.

Vipul at 01:32, 27 October 2007

2007-10-27T01:32:12Z

← Older revision		Revision as of 01:32, 27 October 2007
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	===Symbol-free definition===		===Symbol-free definition===

	A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if the inverse image of any [[compact space\|compact subset]] in the image set, is a compact subset of the domain.		A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if it is [[closed map\|closed]] the inverse image of any [[compact space\|compact subset]] in the image set, is a compact subset of the domain.

Vipul: /* Relation with other properties */

2007-10-27T01:28:44Z

Relation with other properties

← Older revision		Revision as of 01:28, 27 October 2007
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	A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if the inverse image of any [[compact space\|compact subset]] in the image set, is a compact subset of the domain.		A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if the inverse image of any [[compact space\|compact subset]] in the image set, is a compact subset of the domain.

	~~==Relation with other properties==~~

	~~===Weaker properties===~~

	* [[Perfect map]]

Vipul at 01:27, 27 October 2007

2007-10-27T01:27:19Z

← Older revision		Revision as of 01:27, 27 October 2007
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	===Symbol-free definition===		===Symbol-free definition===

	A [[continuous map]] of [[topological space]]s is termed a '''k-map''' if the inverse image of any [[compact space\|compact subset]] in the image set, is a compact subset of the domain.		A [[continuous map]] of [[topological space]]s is termed a '''proper map''' if the inverse image of any [[compact space\|compact subset]] in the image set, is a compact subset of the domain.

	==Relation with other properties==		==Relation with other properties==

	~~===Stronger properties===~~

	* [[Proper map]]

	===Weaker properties===		===Weaker properties===

	* [[Perfect map]]		* [[Perfect map]]

Vipul: K-map moved to Proper map

2007-10-27T01:26:52Z

K-map moved to Proper map

← Older revision	Revision as of 01:26, 27 October 2007
(No difference)

Vipul at 09:46, 18 August 2007

2007-08-18T09:46:40Z

New page

{{topospace property}}

==Definition==

===Symbol-free definition===

A [[continuous map]] of [[topological space]]s is termed a '''k-map''' if the inverse image of any [[compact space|compact subset]] in the image set, is a compact subset of the domain.

==Relation with other properties==

===Stronger properties===

* [[Proper map]]

===Weaker properties===

* [[Perfect map]]