The concept of conditional independence (CI) within the framework of natural conditional functions (NCFs) is studied. An NCF is a function ascribing natural numbers to possible states of the world; it is the central concept of Spohn's theory of deterministic epistemology. Basic properties of CI within this framework are recalled, and further results analogous to the results concerning probabili...

Answering a question of Sakai, we show that the minimal cardinality of a set of reals X such that Cp(X) does not have the Pytkeev property is equal to the pseudo-intersection number p. Our approach leads to a natural characterization of the Pytkeev property of Cp(X) by means of a covering property of X, and to a similar result for the Reznichenko property of Cp(X).

We consider a (finite or infinite) family of closed convex sets with nonempty intersection in a normed space. A property relating their epigraphs with their intersection’s epigraph is studied, and its relations to other constraint qualifications (such as the linear regularity, the strong CHIP, and Jameson’s (G)-property) are established. With suitable continuity assumption we show how this prop...

In this paper, we analyze the various strengthening and weakening of uniqueness Hahn–Banach extension. addition, consider case in which Y is an ideal X. context, study property (U)/(SU)/(HB) (wU)/(k-U) for a subspace Banach space We obtain new characterizations these properties. different kinds stabilities resulting from properties tensor product spaces, spaces Bochner integrable functions, hig...