On spaces with the ideal convergence property

Jakub Jasinski; Ireneusz Recław

Displaying similar documents to “On spaces with the ideal convergence property”

Erratum to $(δ, 2)$ -primary ideals of a commutative ring

Gülşen Ulucak, Ece Yetkin Çelikel (2020)

Czechoslovak Mathematical Journal

Similarity:

Fixed-place ideals in commutative rings

Ali Rezaei Aliabad, Mehdi Badie (2013)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

Normal restrictions of the noncofinal ideal on $P_{κ} (λ)$

Pierre Matet (2013)

Fundamenta Mathematicae

Similarity:

We discuss the problem of whether there exists a restriction of the noncofinal ideal on $P_{κ} (λ)$ that is normal.

A characterization of the meager ideal

Piotr Zakrzewski (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.

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

Marta Frankowska, Andrzej Nowik (2011)

Colloquium Mathematicae

Similarity:

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.

Ideal convergence and divergence of nets in $(ℓ)$ -groups

Antonio Boccuto, Xenofon Dimitriou, Nikolaos Papanastassiou (2012)

Czechoslovak Mathematical Journal

Similarity:

In this paper we introduce the $ℐ$ - and $ℐ^{*}$ -convergence and divergence of nets in $(ℓ)$ -groups. We prove some theorems relating different types of convergence/divergence for nets in $(ℓ)$ -group setting, in relation with ideals. We consider both order and $(D)$ -convergence. By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived. We prove that $ℐ^{*}$ -convergence/divergence implies $ℐ$ -convergence/divergence for every ideal,...

On nonregular ideals and $z^{\circ}$ -ideals in $C (X)$

F. Azarpanah, M. Karavan (2005)

Czechoslovak Mathematical Journal

Similarity:

The spaces $X$ in which every prime $z^{\circ}$ -ideal of $C (X)$ is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces $X$ , such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime $z^{\circ}$ -ideal in $C (X)$ is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in $C (X)$ a $z^{\circ}$ -ideal? When is every nonregular (prime) $z$ -ideal in $C (X)$ a...

Ideal limits of sequences of continuous functions

Miklós Laczkovich, Ireneusz Recław (2009)

Fundamenta Mathematicae

Similarity:

We prove that for every Borel ideal, the ideal limits of sequences of continuous functions on a Polish space are of Baire class one if and only if the ideal does not contain a copy of Fin × Fin. In particular, this is true for $F_{σ δ}$ ideals. In the proof we use Borel determinacy for a game introduced by C. Laflamme.