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
Instituto de Matemátics, Universidade Federal Fluminense, Rua São Paulo s/n, Rio de Janeiro 24210, Brazil
Received 11 November 1993; Revised 15 December 1993
Copyright © 1996 Nilson C. Bernardes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.