4 papers
Projection bands and atoms in pervasive pre-Riesz spaces
Anke Kalauch, Helena Malinowski
In vector lattices, the concept of a projection band is a basic tool. We deal with projection bands in the more general setting of an Archimedean pre-Riesz space . We relate the…
Pervasive and weakly pervasive pre-Riesz spaces
Anke Kalauch, Helena Malinowski
Pervasive pre-Riesz spaces are defined by means of vector lattice covers. To avoid the computation of a vector lattice cover, we give two distinct intrinsic characterizations of pe…
Order continuous operators on pre-Riesz spaces and embeddings
Helena Malinowski, Anke Kalauch
We investigate properties of order continuous operators on pre-Riesz spaces with respect to the embedding of the range space into a vector lattice cover or, in particular, into its…
Order continuity from a topological perspective
Till Hauser, Anke Kalauch
We study three types of order convergence and related concepts of order continuous maps in partially ordered sets, partially ordered abelian groups and partially ordered vector spa…