Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (4): 511-515.

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The Characteristic of W-complete (W*-complete) on LCS with the Axiom (T0

  

  1. Department of Mathematics, Hulunbeier College, Hulunbeier 021008 China, School of Mathematics, Nankai University

  • Received:2006-12-11 Online:2009-12-30 Published:2023-06-16
  • About author:Lina(1962-), female, native of Hulunbeier, Inner Mongolia, an associate professor of Hulunbeier College, engages in functional analysis.
  • Supported by:
     Supported by the Scientific Research Fund of Colleges of Inner Mongolia(NJ09180);

Abstract: In this paper, it is shown that if a local convex space is weakly complete, then it is complete. Moreover, it shows that a local convex space with the axiom(To) is weakly complete(or weakly* complete) if and only if it is finite dimensional.

Key words: local convex space, weakly complete, weakly* complete, finite dimensional

CLC Number: