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internal point
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(Definition)
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That is $x$ is an internal point of $S$ if whenever $y \in X$ there exists an $\epsilon > 0$ such that $x + ty \in S$ for all $t < \epsilon$ .
If $X$ is a topological vector space and $x$ is in the interior of $S$ , then it is an internal point, but the converse is not true in general. However if $S \subset {\mathbb{R}}^n$ is a convex set then all internal points are interior points and vice versa.
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- H. L. Royden. Real Analysis. Prentice-Hall, Englewood Cliffs, New Jersey, 1988
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"internal point" is owned by jirka.
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Cross-references: interior points, convex set, converse, interior, topological vector space, interval, contains, line, intersection, vector space
This is version 2 of internal point, born on 2004-06-15, modified 2005-03-07.
Object id is 5923, canonical name is InternalPoint.
Accessed 2109 times total.
Classification:
| AMS MSC: | 52A99 (Convex and discrete geometry :: General convexity :: Miscellaneous) |
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Pending Errata and Addenda
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