In this paper, the concepts of pairwise fuzzy Baire bitopological spaces are introduced and characterizations of pairwise fuzzy Baire bitopological spaces are studied. Several examples are given to illustrate the concepts introduced in this paper.

The main result is the following. Let f:X→Y be a continuous mapping of completely Baire space X onto hereditary weakly Preiss-Simon regular Y such that image every open subset resolvable set in Y. Then Baire. classical Hurewicz theorem about closed embedding rational numbers into metrizable spaces generalized to spaces.

We prove that if f is a function belonging to Baire first class on a compact set K/C and each point of K has a (closed) neighborhood where f is the pointwise limit of some sequence of uniformly bounded rational functions, then f on the whole of K is the pointwise limit of a sequence of rational functions uniformly bounded on K. This is an extension of Bishop's localization theorem. As an applic...

We show that if add(null) = c, then the globally Baire and universally measurable chromatic numbers of the graph of any Borel function on a Polish space are equal and at most three. In particular, this holds for the graph of the unilateral shift on [N]N, although its Borel chromatic number is א0. We also show that if add(null) = c, then the universally measurable chromatic number of every treei...