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Difference between revisions of "Kernel of a set"

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#REDIRECT [[Interior of a set]]
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''open kernel of a set $M$''
 
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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]]).
 
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====Comments====
 
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$\langle M \rangle$ 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.
 

Latest revision as of 20:04, 19 December 2015

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How to Cite This Entry:
Kernel of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kernel_of_a_set&oldid=36944
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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