On metrizability of compactoid sets in non-archimedean locally convex spaces
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Date
2008
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Abstract
In 2003 N. De Grande-De Kimpe, J. Kakol and C.Perez-Garcia
using t-frames and some machinery concerning tensor products
proved that compactoid sets in (LM)-spaces are
metrizable.
In this presentation we show a similar result for locally convex spaces
with a L-base. This extends the first mentioned
result since every (LM)-space has a L-base. We show that any compactoid subset of a non-archimedean locally convex space E is metrizable if and only if the dual of E with the topology of the uniform convergence on compactoid subsets of E is of countable type.
Description
These results have been presented at the 10th International Conference on P-Adic and Non-Archimedean
Analysis, Michigan State University, East Lansing, Michigan,
USA, June 30 to July 3, 2008. Next they have been published in the Indag. Mathem., N.S., 19(2008), 563--578.
Sponsor
Adam Mickiewicz University, Poznan, POLAND
Keywords
Compactoid set, Compactoid resolution
Citation
10th International Conference on P-Adic and Non-Archimedean Analysis, Michigan State University, East Lansing, Michigan, USA, June 30 to July 3, 2008