1 citations · 2 across the 9 of their papers we have counts for
10 papers
Order convergence in ordered vector spaces: compactness, atoms, pervasiveness, and ice cream spaces
Eugene Bilokopytov, Mark Roelands, Samuel Tiersma +3
We study order convergence in ordered vector spaces that are not necessarily lattices. In this setting, we consider two generalizations of order convergence on vector lattices, a d…
L-valued integration
Xingni Jiang, Jan Harm van der Walt, Marten Wortel
We develop integration theory for integrating functions taking values into a Dedekind complete unital -algebra with respect to -valued measures. We then…
Locally solid convergence structures
E. Bilokopytov, J. Conradie, V. G. Troitsky +1
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with lo…
L-functional analysis
Eder Kikianty, Miek Messerschmidt, Luan Naude +5
Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars or $\mathbb…
The order bidual of C(X) for a realcompact space
Marcel de Jeu, Jan Harm van der Walt
It is well known that the bidual of for a compact space , supplied with the Arens product, is isometrically isomorphic as a Banach algebra to $\mathrm C(\tilde X)…
Limits of vector lattices
Walt van Amstel, Jan Harm van der Walt
If is a compact Hausdorff space so that the Banach lattice is isometrically lattice isomorphic to a dual of some Banach lattice, then can be decomposed as the $\e…
On order continuous duals of vector lattices of continuous functions on resolvable spaces
Marcel de Jeu, Jan Harm van der Walt
A topological space is called resolvable if it contains a dense subset with dense complement. Using only basic principles, we show that whenever the space has a resolving s…
A Note on the Completeness of Cc(X,Y)
Jan Harm van der Walt
It is known that there are complete, Hausdorff and regular convergence vector spaces X and Y such that Lc(X,Y), the space of continuous linear mappings from X into Y equipped with…
Singularities in Space-time Foam Algebras
Jan Harm van der Walt
In this paper we consider the structure of the singularity sets associated with generalized functions in certain space-time foam algebras of generalized functions. In particular, w…
Beyond Topologies, Part I
Elemer E Rosinger, Jan Harm van der Walt
Arguments on the need, and usefulness, of going beyond the usual Hausdorff-Kuratowski-Bourbaki, or in short, HKB concept of topology are presented. The motivation comes, among othe…