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
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