ThmDex – An index of mathematical definitions, results, and conjectures.

Superconvex and superconvex basic real functions on open basic real interval are continuous

Formulation 0

Let $(a, b) \subseteq \mathbb{R}$ be an D543: Open real interval such that

(i)	$f : (a, b) \to \mathbb{R}$ is a D5606: Subconvex real function
(ii)	$g : (a, b) \to \mathbb{R}$ is a D5607: Superconvex real function

Then

(1)	$f$ is a D5231: Standard-continuous real function
(2)	$g$ is a D5231: Standard-continuous real function