Geodesic
Non-Archimedean free Banach spaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 979-987.

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The article is devoted to the investigation of free Banach spaces over non-Archimedean fields, generated by ultrametrizable spaces $X$. Their isomorfisms with spaces of integrable functions are proved for compact $X$. Non-Archimedean free locally convex spaces generated by uniform spaces $X$ are also considered. 
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S. V. Lyudkovskii. Non-Archimedean free Banach spaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 979-987. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a8/

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