Some observations on filters with properties defined by open covers

Rodrigo Hernández-Gutiérrez; Paul J. Szeptycki

Displaying similar documents to “Some observations on filters with properties defined by open covers”

Guessing clubs in the generalized club filter

Bernhard König, Paul Larson, Yasuo Yoshinobu (2007)

Fundamenta Mathematicae

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We present principles for guessing clubs in the generalized club filter on $_{κ} λ$ . These principles are shown to be weaker than classical diamond principles but often serve as sufficient substitutes. One application is a new construction of a λ⁺-Suslin-tree using assumptions different from previous constructions. The other application partly solves open problems regarding the cofinality of reflection points for stationary subsets of ${[λ]}^{ℵ ₀}$ .

Some properties of state filters in state residuated lattices

Michiro Kondo (2021)

Mathematica Bohemica

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We consider properties of state filters of state residuated lattices and prove that for every state filter $F$ of a state residuated lattice $X$ : (1) $F$ ...

On meager function spaces, network character and meager convergence in topological spaces

Taras O. Banakh, Volodymyr Mykhaylyuk, Lubomyr Zdomsky (2011)

Commentationes Mathematicae Universitatis Carolinae

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For a non-isolated point $x$ of a topological space $X$ let ${nw}_{χ} (x)$ be the smallest cardinality of a family $𝒩$ of infinite subsets of $X$ such that each neighborhood $O (x) \subset X$ of $x$ contains a set $N \in 𝒩$ . We prove that (a) each infinite compact Hausdorff space $X$ contains a non-isolated point $x$ with ${nw}_{χ} (x) = ℵ_{0}$ ; (b) for each point $x \in X$ with ${nw}_{χ} (x) = ℵ_{0}$ there is an injective sequence ${(x_{n})}_{n \in ω}$ in $X$ that $ℱ$ -converges to $x$ for some meager filter $ℱ$ on $ω$ ; (c) if a functionally Hausdorff space $X$ contains an $ℱ$ -convergent injective sequence for some...

Products of topological spaces and families of filters

Paolo Lipparini (2023)

Commentationes Mathematicae Universitatis Carolinae

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We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelöf if and only if all subproducts by $\leq ω_{1}$ factors are Lindelöf. Parallel results are obtained for final $ω_{n}$ -compactness, $[λ, μ]$ -compactness, the Menger and the Rothberger properties.

Filter factors of truncated TLS regularization with multiple observations

Iveta Hnětynková, Martin Plešinger, Jana Žáková (2017)

Applications of Mathematics

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The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems $A x \approx b$ were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of $A$ applied to $b$ . This paper focuses...

The point of continuity property, neighbourhood assignments and filter convergences

Ahmed Bouziad (2012)

Fundamenta Mathematicae

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We show that for some large classes of topological spaces X and any metric space (Z,d), the point of continuity property of any function f: X → (Z,d) is equivalent to the following condition: (*) For every ε > 0, there is a neighbourhood assignment ${(V_{x})}_{x \in X}$ of X such that d(f(x),f(y)) < ε whenever $(x, y) \in V_{y} \times V_{x}$ . We also give various descriptions of the filters ℱ on the integers ℕ for which (*) is satisfied by the ℱ-limit of any sequence of continuous functions from a topological space into a metric...

Filter descriptive classes of Borel functions

Gabriel Debs, Jean Saint Raymond (2009)

Fundamenta Mathematicae

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We first prove that given any analytic filter ℱ on ω the set of all functions f on $2^{ω}$ which can be represented as the pointwise limit relative to ℱ of some sequence ${(f ₙ)}_{n \in ω}$ of continuous functions ( $f = l i m_{ℱ} f ₙ$ ), is exactly the set of all Borel functions of class ξ for some countable ordinal ξ that we call the rank of ℱ. We discuss several structural properties of this rank. For example, we prove that any free Π⁰₄ filter is of rank 1.

$P_{λ}$ -sets and skeletal mappings

Aleksander Błaszczyk, Anna Brzeska (2013)

Colloquium Mathematicae

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We prove that if the topology on the set Seq of all finite sequences of natural numbers is determined by $P_{λ}$ -filters and λ ≤ , then Seq is a $P_{λ}$ -set in its Čech-Stone compactification. This improves some results of Simon and of Juhász and Szymański. As a corollary we obtain a generalization of a result of Burke concerning skeletal maps and we partially answer a question of his.

Relative co-annihilators in lattice equality algebras

Sogol Niazian, Mona Aaly Kologani, Rajab Ali Borzooei (2024)

Mathematica Bohemica

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We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among $\lor$ -irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra $𝔼$ and $𝔽$ a filter of $𝔼$ , we define the set of all $𝔽$ -involutive filters of $𝔼$ and show that by defining some operations on it, it makes a BL-algebra.

An investigation on the $n$ -fold IVRL-filters in triangle algebras

Saeide Zahiri, Arsham Borumand Saeid (2020)

Mathematica Bohemica

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The present study aimed to introduce $n$ -fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of $n$ -fold (positive) implicative IVRL-extended filters and $n$ -fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the $n$ -fold IVRL-extended filters, $n$ -fold (positive) implicative algebras, and the Gödel triangle algebra were discussed. ...

Note on $α$ -filters in distributive nearlattices

Ismael Calomino (2019)

Mathematica Bohemica

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In this short paper we introduce the notion of $α$ -filter in the class of distributive nearlattices and we prove that the $α$ -filters of a normal distributive nearlattice are strongly connected with the filters of the distributive nearlattice of the annihilators.

$G$ -supplemented property in the lattices

Shahabaddin Ebrahimi Atani (2022)

Mathematica Bohemica

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Let $L$ be a lattice with the greatest element $1$ . Following the concept of generalized small subfilter, we define $g$ -supplemented filters and investigate the basic properties and possible structures of these filters.

Generalized prime $D$ -filters of distributive lattices

A.P. Phaneendra Kumar, M. Sambasiva Rao, K. Sobhan Babu (2021)

Archivum Mathematicum

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The concept of generalized prime $D$ -filters is introduced in distributive lattices. Generalized prime $D$ -filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime $D$ -filters is introduced in distributive lattices and properties of minimal prime $D$ -filters are then studied with respect to congruences. Some topological properties of the space of all prime $D$ -filters of a distributive lattice are also studied.

On embedding models of arithmetic of cardinality ℵ₁ into reduced powers

Juliette Kennedy, Saharon Shelah (2003)

Fundamenta Mathematicae

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In the early 1970’s S. Tennenbaum proved that all countable models of PA₁¯ + ∀₁ -Th(ℕ) are embeddable into the reduced product $ℕ^{ω} / ℱ$ , where ℱ is the cofinite filter. In this paper we show that if M is a model of PA¯ + ∀₁ - Th(ℕ), and |M| = ℵ₁, then M is embeddable into $ℕ^{ω} / D$ , where D is any regular filter on ω.

Connected components of sets of finite perimeter and applications to image processing

Luigi Ambrosio, Vicent Caselles, Simon Masnou, Jean-Michel Morel (2001)

Journal of the European Mathematical Society

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This paper contains a systematic analysis of a natural measure theoretic notion of connectedness for sets of finite perimeter in $ℝ^{N}$ , introduced by H. Federer in the more general framework of the theory of currents. We provide a new and simpler proof of the existence and uniqueness of the decomposition into the so-called $M$ -connected components. Moreover, we study carefully the structure of the essential boundary of these components and give in particular a reconstruction formula of a set...