Covering properties for s with nested bases.
The aim of the paper is to introduce and study a new class of spaces called mildly -normal spaces and a new class of functions called --continuous, --map, almost -continuous function and almost --closed function in bitopological spaces. Subsequently, the relationships between mildly -normal spaces and the new bitopological functions are investigated. Moreover, we obtain characterizations of mildly -normal spaces, properties of the new bitopological functions and preservation theorems for...
We say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that is a quasi-Baire space iff , is a pairwise Baire bitopological space, where , is a quasi-uniformity that determines, in . Nachbin’s sense, the topological ordered space .