EDB — 17B

[17B] Prerequisites:[0GJ]↺↻.Difficulty:*.

Given \(A⊂ ℝ^ n\) convex, show that \({{A}^\circ }={{\Big(\overline A\Big)}^\circ }\) (the inner part of the closure of \(A\)).

Using [17J]↺↻ it is easily shown that \({{A}^\circ }⊇ {{\Big(\overline A\Big)}^\circ }\); unfortunately this result is useful in one of the possible proofs of [17J]↺↻ (!); an alternative proof uses simplexes as neighbourhoods, cf [16Z]↺↻.