The paper contains a systematic study of the lateral partial order ⊑ in a Riesz space (the relation x⊑y means that x is a fragment of y) with applications to nonlinear analysis of Riesz spaces. We introduce and study lateral ...

We construct a separately continuous function e:E×K→{0,1} on the product of a Baire space E and a compact space K such that no restriction of e to any non-meagre Borel set in E×K is continuous. The function e has no points ...