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Relative interior : ウィキペディア英語版
Relative interior
In mathematics, the relative interior of a set is a refinement of the concept of the interior, which is often more useful when dealing with low-dimensional sets placed in higher-dimensional spaces. Intuitively, the relative interior of a set contains all points which are not on the "edge" of the set, relative to the smallest subspace in which this set lies.
Formally, the relative interior of a set ''S'' (denoted \operatorname(S)) is defined as its interior within the affine hull of ''S''. In other words,
:\operatorname(S) := \,
where \operatorname(S) is the affine hull of ''S'', and N_\epsilon(x) is a ball of radius \epsilon centered on x. Any metric can be used for the construction of the ball; all metrics define the same set as the relative interior.
For any nonempty convex sets C \subseteq \mathbb^n the relative interior can be defined as
:\operatorname(C) := \: \lambda x + (1-\lambda)y \in C\}.
== See also ==

* Interior (topology)
* Algebraic interior
* Quasi-relative interior

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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