Strict Topology on Spaces of Continuous Vector-Valued Functions
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 890-896

Voir la notice de l'article provenant de la source Cambridge University Press

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.
Choo, Seki A. Strict Topology on Spaces of Continuous Vector-Valued Functions. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 890-896. doi: 10.4153/CJM-1979-084-9
@article{10_4153_CJM_1979_084_9,
     author = {Choo, Seki A.},
     title = {Strict {Topology} on {Spaces} of {Continuous} {Vector-Valued} {Functions}},
     journal = {Canadian journal of mathematics},
     pages = {890--896},
     year = {1979},
     volume = {31},
     number = {4},
     doi = {10.4153/CJM-1979-084-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-084-9/}
}
TY  - JOUR
AU  - Choo, Seki A.
TI  - Strict Topology on Spaces of Continuous Vector-Valued Functions
JO  - Canadian journal of mathematics
PY  - 1979
SP  - 890
EP  - 896
VL  - 31
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-084-9/
DO  - 10.4153/CJM-1979-084-9
ID  - 10_4153_CJM_1979_084_9
ER  - 
%0 Journal Article
%A Choo, Seki A.
%T Strict Topology on Spaces of Continuous Vector-Valued Functions
%J Canadian journal of mathematics
%D 1979
%P 890-896
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-084-9/
%R 10.4153/CJM-1979-084-9
%F 10_4153_CJM_1979_084_9

[1] 1. Arens, R., Extension of functions on fully normal spaces, Pacific J. Math.. 2 (1952), 11–22. Google Scholar

[2] 2. Bourbaki, N., Integration, Chap. IX, Elements de Mathématiques 35 (Hermann, Paris, 1969). Google Scholar

[3] 3. Buck, R. C., Bounded continuous functions on a locally compact space, Mich. Math. J., 5 (1958), 95–104. Google Scholar

[4] 4. Collins, H. S., On the space r(S), with the strict topology, Math. Zeit.. 106 (1968), 361–373. Google Scholar

[5] 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] 6. Fontenot, R. A., Strict topologies for vector-valued functions, Can. J. Math.. 26 (1974), 841–853. Google Scholar

[7] 7. Husain, T., The open mapping and closed graph theorems in topological'vector spaces (Clarendon Press, Oxford, 1905). Google Scholar

[8] 8. Katsaras, A., Spaces of vector measures, Trans. Amer. Math. Soc. 206 (1975), 313–328. Google Scholar

[9] 9. Kelly, J. L., General topology (Van Nostrand, Princeton, N.J., 1955). Google Scholar

[10] 10. Khurana, S. S. and Choo, S. A., Strict topology and P-spaces, Proc. Amer. Math. Soc. 61 (1970), 280–284. Google Scholar

[11] 11. Schaefer, H. H., Topological vector spaces (MacMillan, New York, 1966). Google Scholar

[12] 12. Schuchat, A. H., Integral representation theorems in topological vector spaces, Trans. Amer. Math. Soc. 172 (1972), 376–397. Google Scholar

[13] 13. Sentllles, F. D., Bounded continuous functions on a completely regular space, Trans. Amer. Math. Soc. 168 (1972), 311–336. Google Scholar

[14] 14. Wells, J., Bounded continuous vector-valued functions on a locally compact space, Michigan Math. J.. 12 (1965), 119–126. Google Scholar

Cité par Sources :