By the Kuratowski-Ulam theorem, if A subset of Rn+1 = R-n x R is a Borel set which has second category intersection with every ball (i.e., is "everywhere second category"), then there is a y is an element of R such that the section A boolean AND (R-n x {y}) is everywhere second category in...

Diamond, Pomerance and Rubel (1981) proved that there are subsets M of the complex plane such that for any two entire functions f and g if f[M] = g[M], then f = g. Baraducci and Dikranjan showed in 1993 that the continuum hypothesis (CH) implies the existence of a similar set M subset of R for the c...

In this paper we investigate two main problems. One of them is the question on the existence of category liftings in the product of two topological spaces. We prove, that if X x Y is a Baire space, then, given (strong) category liftings rho and sigma on X and Y, respectively, there exists a (strong)...

We study the class of Tychonoff spaces that can be mapped continuously into R in such a way that the preimage of every nowhere dense set is nowhere dense. We show that every metric space without isolated points is in this class. We also give examples of spaces which have nowhere constant continuous ...

This paper continues the investigation begun in [M.R. Burke, Topology Appl. 129 (2003) 29-65] into the measurability properties of separately continuous functions. We sharpen several results from that paper. (1) If X is any product of countably compact Dedekind complete linearly ordered spaces, then...

We prove that it is relatively consistent with ZFC that in any perfect Polish space, for every nonmeager set A there exists a nowhere dense Cantor set C such that A boolean AND C is nonmeager in C. We also examine variants of this result and establish a measure theoretic analog.