Titlebook: An Introduction to the Theory of Functional Equations and Inequalities; Cauchy‘s Equation an Marek Kuczma,Attila Gilányi Textbook 2009Lates

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Set Theorydamental role in the entire book. The mere existence of discontinuous additive functions and discontinuous convex functions depends on that axiom. Therefore the axiom of choice will equally be treated with the remaining axioms of the set theory and no special mention will be made whenever it is used.

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Boundedness and Continuity of Convex Functions and Additive Functions⊂ . is open and non-empty, and f is bounded above on T, then . is continuous in . Are there other sets . with this property? What are possibly weak conditions which assure the continuity of a convex function, or of an additive function? In this and in the next chapter we will deal with such questions.

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Auswirkungen auf das Informationssystem,In 2.1–2.2 . is a topological space, so, e.g., . may be a metric space, or, in particular, ℝ.. A set . ⊂ . is called . iff int cl . = ⊘. A set . ⊂ . is said to be of the . iff . is a countable union of nowhere dense sets:

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