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On the continuity of functions. (English) Zbl 1155.26314

Summary: Some theorems on continuity are presented. First we will prove that every convex function \(f\:\mathbb R^n\to\mathbb R\) is continuous using nonstandard analysis methods. Then we prove that if the image of every compact (resp. convex) is compact (resp. convex), then the function is continuous.

MSC:

26E35 Nonstandard analysis
52A41 Convex functions and convex programs in convex geometry
54C05 Continuous maps
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