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, Volume 21, Issue 2, pp 117–133 | Cite as

Bornological and ultrabornological C(X;E) spaces

  • Jean Schmets


Denote by Cs(X;E) the space of the continuous functions defined on the completely regular and Hausdorff space X, with values in the locally convex topological vector space E, when it is endowed with the simple or point-wise convergence topology. We give here some conditions on X and on E under which the space Cs(X;E) is bornological or ultrabornological and characterize in some cases the corresponding associated spaces. We give also a few results concerning the case of the compact connvergence topology.


Continuous Function Vector Space Number Theory Algebraic Geometry Topological Group 
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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Jean Schmets
    • 1
  1. 1.Institut de MathématiqueUniversité de LiègeLiegeBelgium

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