Materiały konferencyjne (WMiI)

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On metrizability of compactoid sets in non-archimedean locally convex spaces
(2008) Kakol, Jerzy; Śliwa, Wiesław
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.