Difference between revisions of "Interior of a set"
From Encyclopedia of Mathematics
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The set of interior points of $X$ (cf. [[Interior point of a set|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. | The set of interior points of $X$ (cf. [[Interior point of a set|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. | ||
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Revision as of 17:15, 14 October 2014
$X$ 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=33643
Interior of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Interior_of_a_set&oldid=33643
This article was adapted from an original article by S.M. Sirota (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article