Difference between revisions of "Interior point of a set"
From Encyclopedia of Mathematics
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A point $x$ 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 $A$. | A point $x$ 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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Latest revision as of 21:24, 15 December 2015
2020 Mathematics Subject Classification: Primary: 54A [MSN][ZBL]
in a topological space
A point $x$ 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=33638
Interior point of a set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Interior_point_of_a_set&oldid=33638
This article was adapted from an original article by S.M. Sirota (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article