Difference between revisions of "Kernel of a set"
From Encyclopedia of Mathematics
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''open kernel of a set $M$'' | ''open kernel of a set $M$'' | ||
| − | The set $\langle M \rangle$ of all interior points of $M$. 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. [[ | + | 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==== | ====Comments==== | ||
| − | $\langle M \rangle$ is usually called the interior of $M$ (cf. [[ | + | $\langle M \rangle$ 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. |
Revision as of 21:20, 15 December 2015
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
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