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The H S P -Classes of Archimedean l -groups with Weak Unit

Bernhard Banaschewski, Anthony Hager (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

W denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar H , S , and P from universal algebra are here meant in W . and denote the integers and the reals, with unit 1, qua W -objects. V denotes a non-void finite set of positive integers. Let 𝒢 W be non-void and not { { 0 } } . We show(1) H S P 𝒢 = H S P ( H S 𝒢 S ) , and(2) W 𝒢 = H S P 𝒢 if and only if V ( 𝒢 = H S P { 1 v | v V } ) . Our proofs are, for the most part, simple calculations. There is no real use of methods of universal algebra (e.g., free objects), and only one restricted...

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 structure of transitive ordered permutation groups

Zhu, Zuo-Tong, Huang Zhenyu (1999)

Czechoslovak Mathematical Journal

We give some necessary and sufficient conditions for transitive l -permutation groups to be 2 -transitive. We also discuss primitive components and give necessary and sufficient conditions for transitive l -permutation groups to be normal-valued.

Topological automorphism groups of chains.

Sergei V. Ovchinnikov (2001)

Mathware and Soft Computing

It is shown that any set-open topology on the automorphism group A(X) of a chain X coincides with the pointwise topology and that A(X) is a topological group with respect to this topology. Topological properties of connectedness and compactness in A(X) are investigated. In particular, it is shown that the automorphism group of a doubly homogeneous chain is generated by any neighborhood of the identity element.

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.

Currently displaying 301 – 320 of 449