Displaying similar documents to “More than a 0-point”

On spaces with the ideal convergence property

Jakub Jasinski, Ireneusz Recław (2008)

Colloquium Mathematicae

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Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to I b , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.

More on cardinal invariants of analytic P -ideals

Barnabás Farkas, Lajos Soukup (2009)

Commentationes Mathematicae Universitatis Carolinae

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Given an ideal ℐ on ω let 𝔞 ( ℐ ) ( 𝔞 ¯ ( ℐ ) ) be minimum of the cardinalities of infinite (uncountable) maximal ℐ -almost disjoint subsets of [ ω ] ω . We show that 𝔞 ( ℐ h ) > ω if ℐ h is a summable ideal; but 𝔞 ( 𝒵 μ → ) = ω for any tall density ideal 𝒵 μ → including the density zero ideal 𝒵 . On the other hand, you have 𝔟 ≤ 𝔞 ¯ ( ℐ ) for any analytic P -ideal ℐ , and 𝔞 ¯ ( 𝒵 μ → ) ≤ 𝔞 for each density ideal 𝒵 μ → . For each ideal ℐ on ω denote 𝔟 ℐ and 𝔡 ℐ the unbounding and dominating numbers of 〈 ω ω , ≤ ℐ 〉 where f ≤ ℐ g iff { n ∈ ω : f ( n ) > g ( n ) } ∈ ℐ . We show that 𝔟 ℐ = 𝔟 and 𝔡 ℐ = 𝔡 for each analytic P -ideal ℐ . Given a Borel...

Fixed-place ideals in commutative rings

Ali Rezaei Aliabad, Mehdi Badie (2013)

Commentationes Mathematicae Universitatis Carolinae

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Let I be a semi-prime ideal. Then P ∘ ∈ Min ( I ) is called irredundant with respect to I if I ≠ ⋂ P ∘ ≠ P ∈ Min ( I ) P . If I is the intersection of all irredundant ideals with respect to I , it is called a fixed-place ideal. If there are no irredundant ideals with respect to I , it is called an anti fixed-place ideal. We show that each semi-prime ideal has a unique representation as an intersection of a fixed-place ideal and an anti fixed-place ideal. We say the point p ∈ β X is a fixed-place point if O p ( X ) is a fixed-place ideal. In...

The ideal (a) is not G δ generated

Marta Frankowska, Andrzej Nowik (2011)

Colloquium Mathematicae

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We prove that the ideal (a) defined by the density topology is not G δ generated. This answers a question of Z. Grande and E. Strońska.

C ( X ) can sometimes determine X without X being realcompact

Melvin Henriksen, Biswajit Mitra (2005)

Commentationes Mathematicae Universitatis Carolinae

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As usual C ( X ) will denote the ring of real-valued continuous functions on a Tychonoff space X . It is well-known that if X and Y are realcompact spaces such that C ( X ) and C ( Y ) are isomorphic, then X and Y are homeomorphic; that is C ( X ) X . The restriction to realcompact spaces stems from the fact that C ( X ) and C ( υ X ) are isomorphic, where υ X is the (Hewitt) realcompactification of X . In this note, a class of locally compact spaces X that includes properly the class of locally...

A characterization of the meager ideal

Piotr Zakrzewski (2015)

Commentationes Mathematicae Universitatis Carolinae

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We give a classical proof of the theorem stating that the σ -ideal of meager sets is the unique σ -ideal on a Polish group, generated by closed sets which is invariant under translations and ergodic.