Bornological linearly topologized modules over a discrete valuation ring
Subject Areas : Functional analysis
D. P.
Pombo Jr.
1
(nstituto de Matemática e Estat´ıstica, Universidade Federal Fluminense, Rua Professor Marcos Waldemar de Freitas Reis, s/no, Bloco G, Campus do Gragoatá, 24210-201, Niterói, RJ, Brazil)
Keywords: Discrete valuation rings, linearly topologized modules, continuity of linear mappings,
Abstract :
‎In this work the notion of a bornological linearly topologized mo\-dule over a discrete valuation ring is introduced and it is shown that certain semimetrizable linearly topologized modules are bornological‎. ‎The main result is a characterization of bornological linearly topologized modules‎, ‎from which the completeness and the quasi-completeness of certain linearly topologized modules of continuous linear mappings are derived.
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