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Paper   IPM / M / 2944
School of Mathematics
  Title:   On nonregular ideals and z0-ideals in C(X)
1.  F. Azarpanah
2.  M. Karavan
  Status:   Published
  Journal: Czechoslovak Math. J.
  Vol.:  55(130)
  Year:  2005
  Pages:   397-407
  Supported by:  IPM
The spaces X in which every prime z°-ideal of C(X) is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces X, such as metric spaces, basically disconnected spaces and one-point compactification of discrete spaces, every prime z°-ideal in C(X) is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in C(X) a z°-ideal? When is every nonregular (prime) z-ideal in C(X) a z°-ideal? For instance, we have shown that every nonregular prime ideal of C(X) is a z°-ideal if and only if X is ∂-space (a space in which the boundary of any zeroset is again a zeroset).

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