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Strict Topology on Spaces of Continuous Vector-Valued Functions

Published online by Cambridge University Press:  20 November 2018

Seki A. Choo
Seki A. Choo*
Affiliation:
Manchester College, North Manchester, Indiana
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In this paper, X denotes a completely regular Hausdorff space, Cb(X) all real-valued bounded continuous functions on X, E a Hausforff locally convex space over reals R, Cb(X, E) all bounded continuous functions from X into E, Cb(X) ⴲ E the tensor product of Cb(X) and E. For locally convex spaces E and F, E ⴲ, F denotes the tensor product with the topology of uniform convergence on sets of the form S X T where S and T are equicontinuous subsets of E′, F′ the topological duals of E, F respectively ([11], p. 96). For a locally convex space G , G ′ will denote its topological dual.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 4 , 01 August 1979 , pp. 890 - 896
Copyright
Copyright © Canadian Mathematical Society 1979

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