nLab
interior

Contents

Definition

For SXS \subset X a subset of a topological space XX, a, interior point of SS is a point xSx \in S which has a neighbourhood in XX that is contained in SS. The union of all interior points is the interior S S^\circ of SS.

In general, we have S SS^\circ \subseteq S. SS is open if and only if S =SS^\circ = S.

Compare the topological closure S¯\bar{S} and frontier S=S¯S \partial S = \bar{S} \setminus S^\circ.

Revised on October 14, 2010 03:40:46 by Toby Bartels (76.85.201.22)