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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 set in a topological space $X$ is a regular open or [[Canonical set|canonical set]]. Spaces in which the open canonical sets form a [[Base|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.
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#REDIRECT [[Interior of a set]]
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See also [[Interior of a set|Interior of a set]].
 

Latest revision as of 20:14, 19 December 2015

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How to Cite This Entry:
Interior. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Interior&oldid=33639
This article was adapted from an original article by V.I. Ponomarev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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