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What (who) is 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 .

https://en.wikipedia.org/wiki/Closure_(topology)

Closed city

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.

https://en.wikipedia.org/wiki/Closed_city

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.

https://en.wikipedia.org/wiki/Closed_set

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.

https://en.wikipedia.org/wiki/Closure (topology)