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Some conditions implying the continuity of $$t$$-Wright convex functions. (English) Zbl 1109.26002
Let $$X$$ be a real linear topological space, $$D\subseteq X$$ be an open convex set and $$f:D \to R$$ be a $$t$$-Wright convex function. Sufficient conditions upon these data are given (in terms of a second category Baire subset $$T\subseteq D$$) which ensure that $$f$$ is continuous and convex over $$D$$.

##### MSC:
 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 26A51 Convexity of real functions in one variable, generalizations 39B62 Functional inequalities, including subadditivity, convexity, etc.