Displaying similar documents to “Topological characterizations of ordered groups with quasi-divisor theory”

The quasi Isbell topology on function spaces

D. N. Georgiou, A. C. Megaritis (2015)

Colloquium Mathematicae

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In this paper, on the family (Y) of all open subsets of a space Y we define the so called quasi Scott topology, denoted by τ q S c . This topology defines in a standard way, on the set C(Y,Z) of all continuous maps of the space Y to a space Z, a topology t q I s called the quasi Isbell topology. The latter topology is always larger than or equal to the Isbell topology, and smaller than or equal to the strong Isbell topology. Results and problems concerning the topology t q I s are given.

Construction of p o -groups with quasi-divisors theory

Jiří Močkoř (2000)

Czechoslovak Mathematical Journal

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A method is presented making it possible to construct p o -groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups H ( Δ , ℤ ) , where Δ are finitely atomic root systems. Some examples of these constructions are presented.

Fine and quasi connectedness in nonlinear potential theory

David R. Adams, John L. Lewis (1985)

Annales de l'institut Fourier

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If B α , p denotes the Bessel capacity of subsets of Euclidean n -space, α > 0 , 1 < p < ∞ , naturally associated with the space of Bessel potentials of L p -functions, then our principal result is the estimate: for 1 < α p ≤ n , there is a constant C = C ( α , p , n ) such that for any set E min { B α , p ( E ∩ Q ) , B α , p ( E c ∩ Q ) } ≤ C · B α , p ( Q ∩ ∂ f E ) for all open cubes Q in n -space. Here ∂ f E is the boundary of the E in the ( α , p ) -fine topology i.e. the smallest topology on c -space that makes the associated ( α , p ) -linear potentials continuous there. As a consequence,...

Quasi-homeomorphisms, Goldspectral spaces and Jacspectral spaces

Othman Echi (2003)

Bollettino dell'Unione Matematica Italiana

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In this paper, we deal with the study of quasi-homeomorphisms, the Goldman prime spectrum and the Jacobson prime spectrum of a commutative ring. We prove that, if g : Y → X is a quasi-homeomorphism, Z a sober space and f : Y → Z a continuous map, then there exists a unique continuous map F : X → Z such that F ∘ g = f . Let X be a T 0 -space, q : X → s X the injection of X onto its sobrification X s . It is shown, here, that q ⁢ Gold ⁢ X = Gold ⁢ X s , where Gold ⁢ X is the set of all locally closed points of X . Some applications are also indicated. The Jacobson prime...

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.