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文章基本信息

  • 标题:The closed neighborhood and filter conditions in solid sequence spaces
  • 本地全文:下载
  • 作者:P. D. Johnson, Jr.
  • 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.
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