Abstract
We take up again the theory of normed spaces and pre-Hilbert spaces. §§1 to 5 are already familiar, excepting possibly Theorem 8.3.4 on equivalent norms. In §§6, 7, 8 we make the connection between this theory and that of complete spaces; some of these results (Banach-Steinhaus theorem, Riesz’s theorem) are very fruitful, but the reader can hardly be convinced of this unless (s)he studies ‘functional analysis’ later on.
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© 1984 Springer Science+Business Media New York
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Dixmier, J. (1984). Normed Spaces. In: General Topology. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4032-5_8
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DOI: https://doi.org/10.1007/978-1-4757-4032-5_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2823-8
Online ISBN: 978-1-4757-4032-5
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