Functional characterizations of p-spaces

We show that a completely regular space Y is a p-space (a ?ech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G _δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.     

Cardinal functions,bornologies and function spaces

We continue the study of topologies of strong uniform convergence on bornologies initiated in Beer and Levi (J Math Anal Appl 350:568–589, 2009, Set-Valued Var Anal 18:251–275, 2010). We study cardinal invariants of topologies of (strong) uniform convergence on bornologies on the space of continuous real-valued functions, and we also generalize some known results from the literature.