Gallego Lupiáñez, Francisco2023-06-202023-06-201988S. Banach, Th6orie des operations lin6aires, 2nd ed., Chelsea, New York, 1978. H. H. Corson, Collections of convex sets which cover a Banach space, Fund. Math. 49 (1961), 143-145. H. H. Corson, T. J. McMinn, E. A. Michael, and J. I.Nagata, Bases and local finiteness, Notices Amer. Math. Soc. 6(1959), 814. D. W. Curtis, Total and absolute paracompactness, Fund. Math. 77 (1973), 277-293. R. M. Ford, Basis properties in dimension theory, Doctoral Dissertation, Auburn Univ., 1963. R. B. Holmes, Geometrical functional analysis and its applications, Springer-Verlag, New York, 1975. J. Horwath, Topological vector spaces and distributions. I, Addison-Wesley, Reading, Mass., 1966. W. Hurewicz and H. Wallrnan, Dimension theory, 5th ed., Princeton Univ. Press, Princeton, N.J., 1941. A. Pelczyn'ski, MR 23 # A2732. H. Toruiiczyk, Smooth partitions of unity on some nonseparable Banach spaces, Studia Math.46 (1973), 43-51.0002-993910.2307/2047553https://hdl.handle.net/20.500.14352/57271The results of this paper are contained in the author's Doctoral Thesis, directed by Professor E. Outerelo, to whom the author expresses his hearty thanks for his help in the preparation of this paper.In this paper, we study some problems related to the Corson theorem. In particular we prove that co does not fulfil such a theorem; hence this theorem is not valid for all infinite-dimensional Banach spaces. We give also generalizations of Corson's theorem for some infinite-dimensional normed spaces.engjournal articlehttps://www.ams.org/journals/proc/1988-103-01/S0002-9939-1988-0938670-6/S0002-9939-1988-0938670-6.pdfhttp://www.ams.org/restricted access5151.1Open basisLocally finite coveringBanach spacesBounded convex setsNormed spacesTotal paracompactness.Topología1210 Topología