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Difference between revisions of "Interior point of a set"

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(Category:General topology)
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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 $x$ is an interior point of a set $A$, then $A$ is said to be a neighbourhood of the point $x$ in the broad sense.
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A point $x$ which of a given set $A$ in a topological space for which there is an open set $U$ such that $x \in U$ and $U$ is a subset of $A$. 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. The [[interior]] of a set $A$ consists of the interior points of $A$.
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[[Category:General topology]]

Revision as of 17:03, 14 October 2014

in a topological space

A point $x$ which of a given set $A$ in a topological space for which there is an open set $U$ such that $x \in U$ and $U$ is a subset of $A$. 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. The interior of a set $A$ consists of the interior points of $A$.

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=33637
This article was adapted from an original article by S.M. Sirota (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article