Search Results

You are looking at 1 - 3 of 3 items for

  • Author or Editor: F. Azarpanah x
  • All content x
Clear All Modify Search

It is shown thatX is finite if and only ifC(X) has a finite Goldie dimension. More generally we observe that the Goldie dimension ofC(X) is equal to the Souslin number ofX. Essential ideals inC(X) are characterized via their corresponding z-filters and a topological criterion is given for recognizing essential ideals inC(X). It is proved that the Fréchet z-filter (cofinite z-filter) is the intersection of essential z-filters. The intersection of idealsO x wherex runs through nonisolated points inX is the socle ofC(X) if and only if every open set containing all nonisolated points is cofinite. Finally it is shown that if every essential ideal inC(X) is a z-ideal thenX is a P-space.

Restricted access
Restricted access