Abstract
Local convergence of a sequence in an lcs E means that the sequence is contained and convergent in the normed space E B associated with some disk B in E. In 10.1, we are going to study a corresponding concept based on an arbitrary homology. 10.2 is devoted to a corresponding notion of completeness, and in 10.3 we deal with some pecularities occurring when the homology under consideration is the equicontinuous compactology on the dual of an les. The corresponding notion of convergence for sequences, and filters, is what we understand by equicontinuous convergence.
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© 1981 B. G. Teubner, Stuttgart
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Jarchow, H. (1981). Local Convergence and Schwartz Spaces. In: Locally Convex Spaces. Mathematische Leitfäden. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-90559-8_10
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DOI: https://doi.org/10.1007/978-3-322-90559-8_10
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-90561-1
Online ISBN: 978-3-322-90559-8
eBook Packages: Springer Book Archive