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Kernel of a set

From Encyclopedia of Mathematics
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2020 Mathematics Subject Classification: Primary: 54A [MSN][ZBL]

open kernel of a set $M$

The set $\langle M \rangle$ of all interior points of $M$, cf. Interior point of a set. If $A$ and $B$ are mutually complementary sets in a topological space $X$, that is, if $B = X \setminus A$, then $X \setminus [A] = \langle B \rangle$ and $X \setminus \langle B \rangle = [ A ]$, where $[A]$ denotes the closure of $A$ (cf. Closure of a set).


Comments

$\langle M \rangle$ is usually called the interior of $M$ (cf. Interior of a set), and is also denoted by $M^\circ$ and $\mathrm{Int}\, M$. The word "kernel" is seldom used in the English mathematical literature in this context.

How to Cite This Entry:
Kernel of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kernel_of_a_set&oldid=33575
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article