Abstract
It is commonly prove in courses of advanced calculus that compact sets in \( \mathbb{R} \) (or more generally \( {\mathbb{R}^n} \)) are characterized by being closed and bounded. In a general topological vector space only one implication is correct. Here and in the future we will assume that our topological vector spaces are Hausdorff.
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© 1984 Springer-Verlag New York Inc.
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Luecking, D.H., Rubel, L.A. (1984). More about C(G) and H(G). In: Complex Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8295-9_4
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DOI: https://doi.org/10.1007/978-1-4613-8295-9_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90993-6
Online ISBN: 978-1-4613-8295-9
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