METRIZABILITY OF COMPACTOID SETS IN NON-ARCHIMEDEAN HAUSDORFF (LM)-SPACES

N. De Grande-De Kimpe, J. Kakol, C. Perez-Garcia

We prove that compactoid subsets of non-archimedean Hausdorff (LM)-spaces are metrizable, the non-archimedean counterpart of a well-known theorem in Functional Analysis over $\Bbb R$ or $\Bbb C$, which was raised by K. Floret in 1980. In this way we also extend and improve the previous result about metrizability of compactoid sets for the particular case of Hausdorff (LB)-spaces, given by N. De Grande-De Kimpe, J. Kakol, C. Perez-Garcia and W.H. Schikhof in [p-adic locally convex inductive limits. In: p-adic Functional Analysis, 159-222, Lecture Notes in Pure and Appl. Math., 192, Marcel Dekker, New York, 1997].