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| − | ''open kernel of a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k0553001.png" />''
| + | #REDIRECT [[Interior of a set]] |
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| − | The set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k0553002.png" /> of all interior points of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k0553003.png" />. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k0553004.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k0553005.png" /> are mutually complementary sets in a topological space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k0553006.png" />, that is, if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k0553007.png" />, then <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k0553008.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k0553009.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k05530010.png" /> denotes the closure of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k05530011.png" /> (cf. [[Closure of a set|Closure of a set]]).
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| − | ====Comments====
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| − | <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k05530012.png" /> is usually called the interior of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k05530013.png" /> (cf. [[Interior of a set|Interior of a set]]), and is also denoted by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k05530014.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/k/k055/k055300/k05530015.png" />. The word "kernel" is seldom used in the English mathematical literature in this context.
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Latest revision as of 20:04, 19 December 2015
How to Cite This Entry:
Kernel of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kernel_of_a_set&oldid=16955
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article