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Displaying similar documents to “An interesting class of ideals in subalgebras of C ( X ) containing C * ( X ) ”

Dimension in algebraic frames, II: Applications to frames of ideals in C ( X )

Jorge Martinez, Eric R. Zenk (2005)

Commentationes Mathematicae Universitatis Carolinae

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This paper continues the investigation into Krull-style dimensions in algebraic frames. Let L be an algebraic frame. dim ( L ) is the supremum of the lengths k of sequences p 0 < p 1 < ⋯ < p k of (proper) prime elements of L . Recently, Th. Coquand, H. Lombardi and M.-F. Roy have formulated a characterization which describes the dimension of L in terms of the dimensions of certain boundary quotients of L . This paper gives a purely frame-theoretic proof of this result, at once generalizing it to frames which are...

On the complexity of some σ -ideals of σ -P-porous sets

Luděk Zajíček, Miroslav Zelený (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let 𝐏 be a porosity-like relation on a separable locally compact metric space E . We show that the σ -ideal of compact σ - 𝐏 -porous subsets of E (under some general conditions on 𝐏 and E ) forms a Π 1 1 -complete set in the hyperspace of all compact subsets of E , in particular it is coanalytic and non-Borel. Our general results are applicable to most interesting types of porosity. It is shown in the cases of the σ -ideals of σ -porous sets, σ - 〈 g 〉 -porous sets, σ -strongly porous sets, σ -symmetrically...