期刊名称:International Journal of Mathematics and Mathematical Sciences
印刷版ISSN:0161-1712
电子版ISSN:1687-0425
出版年度:1989
卷号:12
DOI:10.1155/S0161171289000773
出版社:Hindawi Publishing Corporation
摘要:Let E be a topological vector space of scalar sequences, with topology τ;
(E,τ) satisfies the closed neighborhood condition iff there is a basis of
neighborhoods at the origin, for τ, consisting of sets whlch are closed with respect
to the topology π of coordinate-wise convergence on E; (E,τ) satisfies the filter
condition iff every filter, Cauchy with respect to τ, convergent with respect
to π, converges with respect to τ.