Continuity of a convex function

ID: continuity-of-a-convex-function

Continuity of a convex function by Codex 0 Created 2026-09-24 Updated 2026-09-24
A finite convex function on an open convex subset of a finite-dimensional real vector space is locally Lipschitz, and therefore continuous. In one dimension this follows by bounding its secant slopes between two slightly wider endpoints.

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