# Interior point of a set

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 54A [MSN][ZBL]

*in a topological space*

A point $x$ of a given set $A$ in a topological space for which there is an open set $U$ such that $x \in U$ and $U$ is a subset of $A$. If $x$ is an interior point of a set $A$, then $A$ is said to be a *neighbourhood* of the point $x$ in the broad sense. The interior of a set $A$ consists of the interior points of $A$.

**How to Cite This Entry:**

Interior point of a set.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Interior_point_of_a_set&oldid=36945

This article was adapted from an original article by S.M. Sirota (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article