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单词 BoundedSetinATopologicalVectorSpace
释义

bounded set (in a topological vector space)


DefinitionSuppose B is a subset of a topological vector spaceMathworldPlanetmath V.Then B is a if for every neighborhoodMathworldPlanetmath U ofthe zero vector in V, thereexists a scalar λ such that BλU.

References

  • 1 W. Rudin, Functional AnalysisMathworldPlanetmath,McGraw-Hill Book Company, 1973.
  • 2 F.A. Valentine, Convex sets, McGraw-Hill Book company, 1964.
  • 3 R. Cristescu, Topological vector spaces,Noordhoff International Publishing, 1977.
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