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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.

Information

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

References

1. Arens, R., Extension of functions on fully normal spaces, Pacific J. Math.. 2 (1952), 11–22.Google Scholar
2. Bourbaki, N., Integration, Chap. IX, Elements de Mathématiques 35 (Hermann, Paris, 1969).Google Scholar
3. Buck, R. C., Bounded continuous functions on a locally compact space, Mich. Math. J., 5 (1958), 95–104.Google Scholar
4. Collins, H. S., On the space r(S), with the strict topology, Math. Zeit.. 106 (1968), 361–373.Google Scholar
5. Conway, J. B., The strict topology and compactness in the space of measures. II, Trans. Amer. Math. Soc. 126 (1967), 474–486.Google Scholar
6. Fontenot, R. A., Strict topologies for vector-valued functions, Can. J. Math.. 26 (1974), 841–853.Google Scholar
7. Husain, T., The open mapping and closed graph theorems in topological'vector spaces (Clarendon Press, Oxford, 1905).Google Scholar
8. Katsaras, A., Spaces of vector measures, Trans. Amer. Math. Soc. 206 (1975), 313–328.Google Scholar
9. Kelly, J. L., General topology (Van Nostrand, Princeton, N.J., 1955).Google Scholar
10. Khurana, S. S. and Choo, S. A., Strict topology and P-spaces, Proc. Amer. Math. Soc. 61 (1970), 280–284.Google Scholar
11. Schaefer, H. H., Topological vector spaces (MacMillan, New York, 1966).Google Scholar
12. Schuchat, A. H., Integral representation theorems in topological vector spaces, Trans. Amer. Math. Soc. 172 (1972), 376–397.Google Scholar
13. Sentllles, F. D., Bounded continuous functions on a completely regular space, Trans. Amer. Math. Soc. 168 (1972), 311–336.Google Scholar
14. Wells, J., Bounded continuous vector-valued functions on a locally compact space, Michigan Math. J.. 12 (1965), 119–126.Google Scholar