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Bibliography
Arsove, M. G., and R. E. Edwards: Generalized bases in topological linear spaces. Studia Math.19, 95–113 (1960).
Banach, S.: Théorie des opérations linéaires. Monografje Matematyczne. Warszawa: Seminar. Matem. Uniw. Warsz. 1932.
Bourbaki, N.: Espaces vectoriels topologiques. Paris: Hermann 1953 and 1955.
Buck, R. C.: Bounded continuous functions on a locally compact space. Michigan Math. J.5, 95–104 (1958).
Collins, H. S.: Completeness and compactness in linear topological spaces. Transactions of Amer. Math. Soc.79, 256–280 (1955).
Conway, J. B.: The strict topology and compactness in the space of measures. Bulletin Amer. Math. Soc.72, 75–78 (1966).
—: Subspaces of (C(S), β), the space (l ∞, β) and (H ∞, β). Bulletin Amer. Math. Soc.72, 79–81 (1966).
—: The strict topology and compactness in the space of measures. Trans. Amer. Math. Soc.126, 474–486 (1967).
Day, M. M.: Normed linear spaces. New York: Academic Press 1962.
Edwards, R. E.: Functional analysis. New York: Holt, Rinehart and Winston 1965.
Grothendieck, A.: Sur la completion du dual d'un espace vectoriel topologique. C. R. Acad. Sci. (Paris)230, 605–606 (1950).
—: Sur les applications lineaires faiblement compactes d'espaces du typeC(K). Canadian J. Math.5, 129–173 (1953).
—: Sur les espaces (F) et (DF). Summa Bras. Math.3, 57–122 (1954).
Grothendieck, A.: Produits tensoriels topologiques et espaces nucleaires. Memoirs Amer. Math. Soc.16, 140 pp. (1955).
Husain, T.: Open mapping and closed graph theorems in topological vector spaces. Oxford: Oxford University Press 1965.
Kelley, J. L.: General topology. New York: D. van Nostrand Co. 1955.
—: Linear topological spaces. New York: D. van Nostrand Co. 1963.
Michael, E.: Continuous selections I. Annals Math.63, 361–382 (1956).
Pietsch, A.: Eine neue Charakterisierung der nuklearen lokalkonvexen Räume, II. Math. Nachr.25, 49–58 (1963).
Retherford, J. R.: Some characterizations ofc 0 andl 1. To appear Coll. Math.
Rubel, L., and A. Shields: The space of bounded analytic functions on a region. Annales de l'Institut Fourier (Université de Grenoble)16, 235–277 (1966).
Schaefer, H. H.: Topological vector spaces. New York: MacMillan Co. 1966.
Ju-Kwei Wang: Multipliers of commutative Banach algebras. Pac. J. Math.11, 1131–1149 (1961).
Warner, S.: The topology of compact convergence on continuous function spaces. Duke Math. J.25, 265–282 (1958).
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This research was supported by NSF Grant GP-5854.
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Collins, H.S. On the spacel ∞ (S), with the strict topology. Math Z 106, 361–373 (1968). https://doi.org/10.1007/BF01115085
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DOI: https://doi.org/10.1007/BF01115085