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Algebraic interior : ウィキペディア英語版
Algebraic interior
In functional analysis, a branch of mathematics, the algebraic interior or radial kernel of a subset of a vector space is a refinement of the concept of the interior. It is the subset of points contained in a given set that it is absorbing with respect to, i.e. the radial points of the set. The elements of the algebraic interior are often referred to as internal points.
Formally, if X is a linear space then the algebraic interior of A \subseteq X is
: \operatorname(A) := \left\.
Note that in general \operatorname(A) \neq \operatorname(\operatorname(A)), but if A is a convex set then \operatorname(A) = \operatorname(\operatorname(A)). If A is a convex set then if x_0 \in \operatorname(A), y \in A, 0 < \lambda \leq 1 then \lambda x_0 + (1 - \lambda)y \in \operatorname(A).
== Example ==
If A \subset \mathbb^2 such that A = \ x_2 \leq 0\} then 0 \in \operatorname(A), but 0 \not\in \operatorname(A) and 0 \not\in \operatorname(\operatorname(A)).

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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