Vol. 51, No. 4, pp. 613-615 (1994)
The Weak and Strong Convergence in Metrizable Spaces Over Valued Fields
Jerzy KakolInstitute of Mathematics, A. Mickiewicz University,
Matejki 48/49, 60-769 Poznan - POLAND
Abstract: Its is proved that a metrizable tvs $E$ over a spherically complete non-archimedean non-trivially valued field is non-archimedean iff every weak null-sequence in $E$ is a null-sequence.
Classification (MSC2000): 46A16
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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.