Dense-in-itself
id:
dense-in-itself-234-9666164
title:
Dense-in-itself
text:
In general topology, a subset A of a topological space is said to be dense-in-itself or crowded
if A has no isolated point.
Equivalently, A is dense-in-itself if every point of A is a limit point of A .
Thus A is dense-in-itself if and only if A ⊆ A ′ , where A ′ is the derived set of A . A dense-in-itself closed set is called a perfect set. The notion of dense set is distinct from dense-in-itself. This can sometimes be confusing, as "X is dense in X" is not the same as "X is dense-in-itself".
brand slug:
wiki
category slug:
encyclopedia
description:
Topological subset with no isolated point
original url:
https://en.wikipedia.org/wiki/Dense-in-itself
date created:
date modified:
2023-12-24T23:48:58Z
main entity:
{"identifier":"Q936674","url":"https://www.wikidata.org/entity/Q936674"}
image:
fields total:
13
integrity:
14