More than a 0-point

Jana Flašková

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 $𝔞 (ℐ)$ ( $\bar{𝔞} (ℐ)$ ) 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 $𝔞 (𝒵_{\vec{μ}}) = ω$ for any tall density ideal $𝒵_{\vec{μ}}$ including the density zero ideal $𝒵$ . On the other hand, you have $𝔟 \leq \bar{𝔞} (ℐ)$ for any analytic $P$ -ideal $ℐ$ , and $\bar{𝔞} (𝒵_{\vec{μ}}) \leq 𝔞$ for each density ideal $𝒵_{\vec{μ}}$ . For each ideal $ℐ$ on $ω$ denote $𝔟_{ℐ}$ and $𝔡_{ℐ}$ the unbounding and dominating numbers of $〈 ω^{ω}, \leq_{ℐ} 〉$ where $f \leq_{ℐ} g$ iff ${n \in ω : f (n) > g (n)} \in ℐ$ . 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 $P_{\circ} \in Min (I)$ is called irredundant with respect to $I$ if $I \neq ⋂_{P_{\circ} \neq P \in Min (I)} P$ . 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 $p \in β X$ 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...

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

On spaces with the ideal convergence property

More on cardinal invariants of analytic P -ideals

Fixed-place ideals in commutative rings

The ideal (a) is not G δ generated

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

More on cardinal invariants of analytic $P$ -ideals

The ideal (a) is not $G_{δ}$ generated

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