Displaying similar documents to “Products of topological spaces and families of filters”

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.

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 ≈ 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...

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 ∨ -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.

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.

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 .

Balcar's theorem on supports

Lev Bukovský (2018)

Commentationes Mathematicae Universitatis Carolinae

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In A theorem on supports in the theory of semisets [Comment. Math. Univ. Carolinae 14 (1973), no. 1, 1–6] B. Balcar showed that if σ ⊆ D ∈ M is a support, M being an inner model of ZFC, and 𝒫 ( D ∖ σ ) ∩ M = r ` ` σ with r ∈ M , then r determines a preorder " ⪯ " of D such that σ becomes a filter on ( D , ⪯ ) generic over M . We show that if the relation r is replaced by a function 𝒫 ( D ∖ σ ) ∩ M = f - 1 ( σ ) , then there exists an equivalence relation " ∼ " on D and a partial order on D / ∼ such that D / ∼ is a complete Boolean algebra, σ / ∼ is a generic filter and [ f ( u ) ] ∼ = - ∑ ( u / ∼ ) for...

Coherent ultrafilters and nonhomogeneity

Jan Starý (2015)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the notion of a coherent P -ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a P -point on ω , and show that these ultrafilters exist generically under 𝔠 = 𝔡 . This improves the known existence result of Ketonen [On the existence of P -points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), 91–94]. Similarly, the existence theorem of Canjar [On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1,...

On the mappings 𝒵 A and ℑ A in intermediate rings of C ( X )

Mehdi Parsinia (2018)

Commentationes Mathematicae Universitatis Carolinae

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In this article, we investigate new topological descriptions for two well-known mappings 𝒵 A and ℑ A defined on intermediate rings A ( X ) of C ( X ) . Using this, coincidence of each two classes of z -ideals, 𝒵 A -ideals and ℑ A -ideals of A ( X ) is studied. Moreover, we answer five questions concerning the mapping ℑ A raised in [J. Sack, S. Watson, C and C * among intermediate rings, Topology Proc. 43 (2014), 69–82].

On preimages of ultrafilters in ZF

Horst Herrlich, Paul Howard, Kyriakos Keremedis (2016)

Commentationes Mathematicae Universitatis Carolinae

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We show that given infinite sets X , Y and a function f : X → Y which is onto and n -to-one for some n ∈ ℕ , the preimage of any ultrafilter ℱ of Y under f extends to an ultrafilter. We prove that the latter result is, in some sense, the best possible by constructing a permutation model ℳ with a set of atoms A and a finite-to-one onto function f : A → ω such that for each free ultrafilter of ω its preimage under f does not extend to an ultrafilter. In addition, we show that in ℳ there exists an ultrafilter compact...

A countably cellular topological group all of whose countable subsets are closed need not be ℝ -factorizable

Mihail G. Tkachenko (2023)

Commentationes Mathematicae Universitatis Carolinae

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We construct a Hausdorff topological group G such that ℵ 1 is a precalibre of G (hence, G has countable cellularity), all countable subsets of G are closed and C -embedded in G , but G is not ℝ -factorizable. This solves Problem 8.6.3 from the book “Topological Groups and Related Structures" (2008) in the negative.