Abstract
In this chapter we deal with compactness in general normed linear spaces. The aim is to convey the notion that in normed linear spaces, norm-compact sets are small—both algebraically and topologically.
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Bibliography
Choquet, G. 1969. Lectures on Analysis, Vol. I: Integration and Topological Vector Spaces, J. Marsden, T. Lance, and S. Gelbart (eds.). New York-Amsterdam: W. A. Benjamin.
James, R. C. 1964. Weakly compact sets. Trans. Amer. Math. Soc., 113, 129 – 140.
Kottman, C. A. 1975. Subsets of the unit ball that are separated by more than one. Studia Math., 53, 15 – 27.
Grothendieck, A. 1955. Produits tensorials topologiques et espaces nucléaires. Memoirs Amer. Math. Soc., 16.
Riesz, F. 1918. Über lineare Funktionalgleichungen. Acta Math., 11, 71 – 98.
Tychonoff, A. 1935. Ein Fixpunktsatz. Math. Ann. 111, 767 – 776.
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© 1984 Springer-Verlag New York, Inc.
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Diestel, J. (1984). Riesz’s Lemma and Compactness in Banach Spaces. In: Sequences and Series in Banach Spaces. Graduate Texts in Mathematics, vol 92. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5200-9_1
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DOI: https://doi.org/10.1007/978-1-4612-5200-9_1
Publisher Name: Springer, New York, NY
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