# Interior

From Encyclopedia of Mathematics

The set of all points of a subset of a topological space for which an open set in exists such that . The interior of the set is usually denoted by and represents the largest open set in contained in . The equality holds, where denotes closure in . The interior of a set in a topological space 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.

#### Comments

See also Interior of a set.

**How to Cite This Entry:**

Interior.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Interior&oldid=13174

This article was adapted from an original article by V.I. Ponomarev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article