Abstract
The webs of M. De Wilde [4] have made an enormous contribution to the closed graph theorems in locally convex spaces(lcs). Although webs have a very intricate layered construction, two properties in particular have contributed to the closed graph theorem. First of all, webs possess a strong countability condition in the range space which suitably matches the Baire property of Fréchet spaces in the domain space; as a result the zero neighbourhood filter is mapped to a p-Cauchy filter, a filter attempting to settle down. Secondly webs provide a completeness condition which allow p-Cauchy filters to converge.
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References
R. Beattie, Convergence spaces with webs, Math. Nachr. 116, 159–164 (1984).
R. Beattie, A convenient category for the closed graph theorem, Categorical Topology, Proc. Conference Toledo, Ohio 1983, Heldermann, Berlin, 29–45 (1984).
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© 1988 Plenum Press, New York
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Beattie, R., Butzmann, HP. (1988). Countability, Completeness and the Closed Graph Theorem. In: Stanković, B., Pap, E., Pilipović, S., Vladimirov, V.S. (eds) Generalized Functions, Convergence Structures, and Their Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1055-6_38
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DOI: https://doi.org/10.1007/978-1-4613-1055-6_38
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