Kakol, JerzyŚliwa, Wiesław2010-07-262010-07-26200810th International Conference on P-Adic and Non-Archimedean Analysis, Michigan State University, East Lansing, Michigan, USA, June 30 to July 3, 2008http://hdl.handle.net/10593/507These 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.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.enCompactoid setCompactoid resolution