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Difference between revisions of "Interior point of a set"

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''in a topological space''
 
''in a topological space''
  
A point which belongs to the given set together with some open set which contains it. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i051/i051860/i0518601.png" /> is an interior point of a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i051/i051860/i0518602.png" />, then <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i051/i051860/i0518603.png" /> is said to be a neighbourhood of the point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i051/i051860/i0518604.png" /> in the broad sense.
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A point which belongs to the given set together with some open set which contains it. If $x$ is an interior point of a set $A$, then $A$ is said to be a neighbourhood of the point $x$ in the broad sense.

Revision as of 17:20, 11 April 2014

in a topological space

A point which belongs to the given set together with some open set which contains it. If $x$ is an interior point of a set $A$, then $A$ is said to be a neighbourhood of the point $x$ in the broad sense.

How to Cite This Entry:
Interior point of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Interior_point_of_a_set&oldid=17856
This article was adapted from an original article by S.M. Sirota (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article