Interior

Interior

Interior refers to the set of all points within a subset of a topological space that are not boundary points. It is denoted by the symbol "int" and is defined in the same way as in a metric space. An open set is a set that contains only interior points.From: Principles of Analysis [2018], Modern Engineering Mathematics [2017], A class of optimization problems motivated by rank estimators in robust regression [2022], Handbook of Mathematics for Engineers and Scientists [2019]

Complex Analysis

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Published in Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene, Modern Engineering Mathematics, 2017

Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene

Remark 63. A boundary point may or may not be in S. No point can simultaneously be interior and a boundary point as the definitions of interior point and boundary point are exclusive.The set of all boundary points of S is called the boundary of S, and is denoted by ∂S.Limit point differs from boundary point in that every open disk about the point contains something from S other than the point itself (see Example 268).Every point of a set is either an interior point or a boundary point.

A class of optimization problems motivated by rank estimators in robust regression

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Published in Optimization, 2022

Michal Černý, Miroslav Rada, Jaromír Antoch, Milan Hladík

Given a set , let denote its interior. Recall that is a shorthand for the ith residual of the form . Given a permutation , define Observe that is a convex polyhedron in , that and that whenever . If the polyhedron is full-dimensional, we call it cell.

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A class of optimization problems motivated by rank estimators in robust regression