On the -Vector Sequential Topology on a non-Archimedean Valued Field

Firstly, we will establish the continuity of the addition and scalar multiplication maps for a sequential topology to get a -vector sequential topology and we will show the stability of the local -convexity by going to the sequential topology. Secondly, we will characterize the sequential closure of a kernel of a linear form and prove the geometric Hahn-Banach theorem in a -vector non-Archimedean sequential topology.