Question: Let S be a convex set in a normed linear space. Then int S and are convex. Similarly it can be shown that closure preserves

Let S be a convex set in a normed linear space. Then int S and are convex.
Similarly it can be shown that closure preserves subspaces, cones and linear varieties. For any convex set the line segment joining an interior point to a boundary point lies in the interior (except for the endpoints).

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