Gleason parts and countably generated closed ideals in $H^\infty $

Countably Generated Ideals in Rings of Continuous Functions

1. Results. Scattered results about countably2 generated ideals in C(X) are established in [2] and [4] : Op is countably generated if and only if pEX and p has a countable base of neighborhoods; Op is both prime and countably generated if and only if Mp is principal, and if and only if pEX and p is isolated; no lower prime ideal is countably generated. We generalize these as follows: if Mp is c...

finitely generated closed ideals in H ∞ ( D )

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Forcing with Ideals Generated by Closed Sets

Consider the posets PI = Borel(R) \ I where I is a σ-ideal σ-generated by a projective collection of closed sets. Then the PI extension is given by a single real r of an almost minimal degree: every real s ∈ V [r] is Cohen-generic over V or

On Borel Mappings and Σ-ideals Generated by Closed Sets

We obtain some results about Borel maps with meager fibers on completely metrizable separable spaces. The results are related to a recent dichotomy by Sabok and Zapletal, concerning Borel maps and σ-ideals generated by closed sets. In particular, we give a “classical” proof of this dichotomy. We shall also show that for certain natural σ-ideals I generated by closed sets in compact metrizable s...

A Geometric Characterization of Gleason Parts