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Interior of a set

From Encyclopedia of Mathematics
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$X$ in a topological space $Y$

The set of interior points of $X$ (cf. Interior point of a set). It is usually denoted by $\operatorname{Int}X$. Invariably, $\operatorname{Int}X=X\setminus[Y\setminus X]=X\setminus\operatorname{Fr}x$, where $\operatorname{Fr}$ is the boundary of $X$. The interior of $X$ is also equal to the union of all subsets of $X$ that are open in the entire space. The interior of a set is sometimes known as the open kernel.

How to Cite This Entry:
Interior of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Interior_of_a_set&oldid=14280
This article was adapted from an original article by S.M. Sirota (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article