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Was (wer) ist topologically closed - definition
IN A TOPOLOGICAL SPACE, THE SMALLEST CLOSED SET CONTAINING A GIVEN SET
Topological closure; Topologically closed; Closure of a set; Set closure
Closure (topology)
In topology, the closure of a subset of points in a topological space consists of all points in together with all limit points of . The closure of may equivalently be defined as the union of and its boundary, and also as the intersection of all closed sets containing .
Closed city
![An aerial view of [[Baikonur]], [[Kazakhstan]]](https://commons.wikimedia.org/wiki/Special:FilePath/Baikonuriss.jpg?width=200 "An aerial view of [[Baikonur]], [[Kazakhstan]]")
![Zheleznogorsk]], in [[Krasnoyarsk Krai]], Russia](https://commons.wikimedia.org/wiki/Special:FilePath/Checkpoint in closed city Zheleznogorsk, Krasnoyarsk Krai.jpg?width=200 "Zheleznogorsk]], in [[Krasnoyarsk Krai]], Russia")
![Zvyozdny]], Russia](https://commons.wikimedia.org/wiki/Special:FilePath/Cultural center in closed town Zvezdniy.jpg?width=200 "Zvyozdny]], Russia")
![Washington]], US](https://commons.wikimedia.org/wiki/Special:FilePath/Richland.jpg?width=200 "Washington]], US")
![[[Sarov Monastery]] in [[Sarov]], Russia (1904)](https://commons.wikimedia.org/wiki/Special:FilePath/SarovskyMonasteryUspenskySobor.jpg?width=200 "[[Sarov Monastery]] in [[Sarov]], Russia (1904)")
![A view of [[Severomorsk]], [[Murmansk Oblast]], Russia, which is home to the [[Northern Fleet]].](https://commons.wikimedia.org/wiki/Special:FilePath/Severomorsk (5145531991).jpg?width=200 "A view of [[Severomorsk]], [[Murmansk Oblast]], Russia, which is home to the [[Northern Fleet]].")
![A view of [[Seversk]], Russia](https://commons.wikimedia.org/wiki/Special:FilePath/Seversk Kurchatova.jpg?width=200 "A view of [[Seversk]], Russia")
![A street in [[Snezhinsk]], Russia](https://commons.wikimedia.org/wiki/Special:FilePath/SnezhinskHousesPobedaStreet.jpg?width=200 "A street in [[Snezhinsk]], Russia")
![Snezhnogorsk]], Russia](https://commons.wikimedia.org/wiki/Special:FilePath/Дом-радуга.jpg?width=200 "Snezhnogorsk]], Russia")
SETTLEMENT WHERE SPECIFIC AUTHORIZATION IS REQUIRED TO VISIT
ZATO; Closed cities; Closed town; Closed administrative-territorial formation; Atomgrad; Atomgrads; Atomograd; Закрытые административно-территориальные образования; Zakrytye administrativno-territorial'nye obrazovaniya; Closed administrative-territorial formations; ЗАТО; List of closed cities; Russian closed city; Closed secret city
A closed city or closed town, not to be confused with a gated community, is a settlement where travel or residency restrictions are applied so that specific authorization is required to visit or remain overnight. Such places may be sensitive military establishments or secret research installations that require much more space or internal freedom than is available in a conventional military base.
Closed set
SET WHOSE COMPLEMENT IS AN OPEN SET
Closed subset; Closed (topology); Closed sets; Closed (mathematics)
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points.
Wikipedia
Closure (topology)
In topology, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of S may equivalently be defined as the union of S and its boundary, and also as the intersection of all closed sets containing S. Intuitively, the closure can be thought of as all the points that are either in S or "very near" S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
