The base-normed space of a unital group
The Cantor Extension of a Lexicographic Product of -Groups
The Cauchy extension of an ordered abelian group realized by -valuations
The dual space of a totally ordered abelian group
The equivalence of Boolean prime ideal theorem and a theorem of functional analysis
The essential cover and the absolute cover of a schematic space
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 group of divisibility of
The nonexistence of free complete vector lattices
The -free products of archimedean -groups
The objective of this paper is to give two descriptions of the -free products of archimedean -groups and to establish some properties for the -free products. Specifically, it is proved that -free products satisfy the weak subalgebra property.
The Redfield topology on some groups of continuous functions.
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 space of maximal convex sets
The theory of quasi-divisors on cartesian products
The -property in
The -property of a Riesz space (real vector lattice) is: For each sequence of positive elements of , there is a sequence of positive reals, and , with for each . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “” obtains for a Riesz space of continuous real-valued functions . A basic result is: For discrete , has iff the cardinal , Rothberger’s bounding number. Consequences and...
Topological characterizations of ordered groups with quasi-divisor theory
For an order embedding of a partly ordered group into an -group a topology is introduced on which is defined by a family of valuations on . Some density properties of sets , and ( being -ideals in ) in the topological space are then investigated, each of them being equivalent to the statement that is a strong theory of quasi-divisors.
Topological groups of divisibility
Topological properties and matrix transformations of certain ordered generalized sequence spaces.
Topology on regulators of lattice ordered groups. II: Completely regular regulators
Torsion classes and subdirect products of Carathéodory vector lattices
Torsion theory for lattice-ordered groups Part II: Homogeneous -groups
Totally inhomogeneous lattice ordered groups