International Journal of Mathematics and Mathematical Sciences 
Volume 19 (1996), Issue 1, Pages 205-207
doi:10.1155/S0161171296000300

A note on the continuity of multilinear mappings in topological modules

Nilson C. Bernardes Jr.

 Instituto de Matemátics, Universidade Federal Fluminense, Rua São Paulo s/n, Rio de Janeiro 24210, Brazil
Received 11 November 1993; Revised 15 December 1993

Abstract

In the present note, we obtain a criterion for the equicontinuity of families of multilinear mappings between topological modules. We also give an example which shows that the hypothesis imposed on the neighborhoods of zero is essential for the validity of our theorem.