Namespaces
Variants
Actions

Difference between revisions of "Interior"

From Encyclopedia of Mathematics
Jump to: navigation, search
("closed" missing here, I think)
(Redirecting to Interior of a set)
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
The set of all points $x$ of a subset $A$ of a topological space $X$ for which an open set $U_x$ in $X$ exists such that $x \in U \subset A$. The interior of the set $A$ is usually denoted by $\mathrm{Int}\, A $ and represents the largest open set in $X$ contained in $A$. The equality $\mathrm{Int}\, A = X \setminus [X \setminus A]$ holds, where $[]$ denotes closure in $X$. The interior of a closed set in a topological space $X$ is a regular open or [[canonical set]]. Spaces in which the open canonical sets form a [[base]] for the topology are called semi-regular. Every regular space is semi-regular. The interior is sometimes called the open kernel of the set.
+
#REDIRECT [[Interior of a set]]
−
 
 
−
====Comments====
 
−
See also [[Interior of a set]].
 

Latest revision as of 20:14, 19 December 2015

Redirect to:

How to Cite This Entry:
Interior. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Interior&oldid=33640
This article was adapted from an original article by V.I. Ponomarev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
Retrieved from "https://encyclopediaofmath.org/index.php?title=Interior&oldid=36993"