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Paper   IPM / M / 737
School of Mathematics
  Title:   When the family of functions vanishing at infinity is ideal of C(X)
1.  T. Soundararajan
2.  F. Azarpanah
  Status:   Published
  Journal: Rocky Mountain J. Math.
  No.:  4
  Vol.:  31
  Year:  2001
  Pages:   1133-1140
  Supported by:  IPM
We prove that C(X) is an ideal in C(X) if and only if every open locally compact subset of X is bounded. In particular, if X is a locally compact Hausdorff space, C (X) is an ideal of C(X) if and only if X is a pseudocompact space. It is shown that the existence of some special functions in C (X) causes C(X) not to be an ideal of C(X). Finally we will characterize the spaces X for which C(X) and CK(X), or Cψ (X), coincide.

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