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Difference between revisions of "Proximate point"

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''of a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075540/p0755401.png" /> in a [[Topological space|topological space]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075540/p0755402.png" />''
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''of a set $A$ in a [[Topological space|topological space]] $X$''
  
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A point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075540/p0755403.png" /> such that every neighbourhood of it has non-empty intersection with <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075540/p0755404.png" />. The set of all proximate points forms the closure <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075540/p0755405.png" />, or <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075540/p0755406.png" />, of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075540/p0755407.png" /> (cf. [[Closure of a set|Closure of a set]]).
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A point $x$ such that every neighbourhood of it has non-empty intersection with $A$. The set of all proximate points forms the closure $[A]$, or $\bar A$, of $A$ (cf. [[Closure of a set|Closure of a set]]).

Latest revision as of 17:15, 11 April 2014

of a set $A$ in a topological space $X$

A point $x$ such that every neighbourhood of it has non-empty intersection with $A$. The set of all proximate points forms the closure $[A]$, or $\bar A$, of $A$ (cf. Closure of a set).

How to Cite This Entry:
Proximate point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Proximate_point&oldid=16532
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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