Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (3): 644-648.

• Articles • Previous Articles     Next Articles

The Smooth Point in C(Ω)

 WANG Rui-Dong   

  1. Science of College, Tianjin University of Technology, Tianjin 300191
  • Received:2008-06-20 Revised:2010-01-15 Online:2010-05-25 Published:2010-05-25
  • Supported by:

    国家自然科学基金(10871090)和高校博士点基金(20060055010)资助

Abstract:

In this paper, we study the smooth point (peak function) in space of C(Ω), where Ω is compact Hausdorff space. We give an example to show that there exists compact Hausdorff space Ω1 such that the smooth point of C1) is dense in the whole space. And we give an counter example to show that there exists compact Hausdorff space Ω2 such that the smooth point of C2) is empty. Finally we give an intrinsic character of the smooth point of space C(Ω) is dense in the whole space.

Key words: Smooth point, Peak function, C(Ω) space

CLC Number: 

  • 46B20
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