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On the Cauchy difference on normed spaces

  • J. Brzdçk
Article

Abstract

LetX be a real linear normed space, (G, +) be a topological group, andK be a discrete normal subgroup ofG. We prove that if a continuous at a point or measurable (in the sense specified later) functionf:XG fulfils the condition:f(x +y) -f(x) -f(y) ∈K whenever ‖x‖ = ‖y‖, then, under some additional assumptions onG,K, andX, there esists a continuous additive functionA :XG such thatf(x) -A(x) ∈K.

Keywords

Normed Space Open Neighbourhood Topological Group Product Space Neighbourhood Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Mathematische Seminar 1996

Authors and Affiliations

  • J. Brzdçk
    • 1
  1. 1.Department of MathematicsPedagogical UniversityPoland

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