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Subgroups and hulls of Specker lattice-ordered groups

Paul F. Conrad, Michael R. Darnel (2001)

Czechoslovak Mathematical Journal

In this article, it will be shown that every -subgroup of a Specker -group has singular elements and that the class of -groups that are -subgroups of Specker -group form a torsion class. Methods of adjoining units and bases to Specker -groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker -group.

The essential cover and the absolute cover of a schematic space

Wolfgang Rump, Yi Chuan Yang (2009)

Colloquium Mathematicae

A theorem of Gleason states that every compact space admits a projective cover. More generally, in the category of topological spaces with continuous maps, covers exist with respect to the full subcategory of extremally disconnected spaces. Such a cover of a space is called its absolute. We prove that the absolute exists within the category of schematic spaces, i.e. the spaces underlying a scheme. For a schematic space, we use the absolute to generalize Bourbaki's concept of irreducible component,...

The 𝒜 r -free products of archimedean l -groups

Dao Rong Tong (1998)

Czechoslovak Mathematical Journal

The objective of this paper is to give two descriptions of the 𝒜 r -free products of archimedean -groups and to establish some properties for the 𝒜 r -free products. Specifically, it is proved that 𝒜 r -free products satisfy the weak subalgebra property.

The Redfield topology on some groups of continuous functions.

Nadal Batle Nicolau, Josep Grané Manlleu (1977)

Stochastica

The Redfield topology on the space of real-valued continuous functions on a topological space is studied (we call it R-topology for short). The R-neighbourhoods are described relating them to the connectedness for the carriers. The main results are: If the space is totally disconnected without isolated points, the R-topology is not discrete. Under suitable conditions on the space, R-convergence implies pointwise or uniform convergence. Under some restrictions, R-convergence for a net implies that...

The σ -property in C ( X )

Anthony W. Hager (2016)

Commentationes Mathematicae Universitatis Carolinae

The σ -property of a Riesz space (real vector lattice) B is: For each sequence { b n } of positive elements of B , there is a sequence { λ n } of positive reals, and b B , with λ n b n b for each n . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “ σ ” obtains for a Riesz space of continuous real-valued functions C ( X ) . A basic result is: For discrete X , C ( X ) has σ iff the cardinal | X | < 𝔟 , Rothberger’s bounding number. Consequences and...

Topological characterizations of ordered groups with quasi-divisor theory

Jiří Močkoř (2002)

Czechoslovak Mathematical Journal

For an order embedding G h Γ of a partly ordered group G into an l -group Γ a topology 𝒯 W ^ is introduced on Γ which is defined by a family of valuations W on G . Some density properties of sets h ( G ) , h ( X t ) and ( h ( X t ) { h ( g 1 ) , , h ( g n ) } ) ( X t being t -ideals in G ) in the topological space ( Γ , 𝒯 W ^ ) are then investigated, each of them being equivalent to the statement that h is a strong theory of quasi-divisors.

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