On the Cauchy difference on normed spaces

  • J. Brzdçk


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.


Normed Space Open Neighbourhood Topological Group Product Space Neighbourhood Versus 
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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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