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Computation of the z-radical in C(X)
Published/Copyright:
May 8, 2006
Abstract
We say that a Tychonoff space X has computable z-radicals if for all ideals
of C(X), the smallest z-ideal containing
is generated as an ideal by all the s ○ f, where f is in
and s is a continuous function ℝ → ℝ with s-1(0) = {0}. We show that every cozero set of a compact space has computable z-radicals and that a subset X of ℝn has computable z-radicals if and only if X is locally closed.
Received: 2003-12-14
Revised: 2005-02-23
Published Online: 2006-05-08
Published in Print: 2006-01-26
© Walter de Gruyter
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Articles in the same Issue
- One jump Weierstrass gap sequence
- Finite projective planes of order n with a 2-transitive orbit of length n – 3
- Maximal arcs in PG(2, q) and partial flocks of the quadratic cone
- The geometry of k-harmonic manifolds
- Radii minimal projections of polytopes and constrained optimization of symmetric polynomials
- On the distance between the axes of elliptic elements generating a free product of cyclic groups
- Bad loci of free linear systems
- CR singularities of real threefolds in ℂ4
- Computation of the z-radical in C(X)
