Inextensible Riesz spaces

Source abstract

My aim in this paper is to give an abstract characterization of the C ∞ spaces described in (6) or (9), and to develop some of the remarkable special properties of these spaces. Although the subject is in some ways highly specialized, inextensible and sequentially inextensible spaces seem common enough (they include all spaces of the forms R x and L 0 ) to be worth studying, and I have already employed them in the proof of more general results (1). In the first section I set out those properties that can be described in simple Riesz space terms; much of this work has already been published in slightly different forms. In the second part I go on to questions that arise when we impose a topology on an inextensible Riesz space. Finally, in the third section, I discuss some problems, arising from the work before, which are related to the famous measurable cardinal problem.