Decomposition of openness.
Decreasing (G) spaces
We consider the class of decreasing (G) spaces introduced by Collins and Roscoe and address the question as to whether it coincides with the class of decreasing (A) spaces. We provide a partial solution to this problem (the answer is yes for homogeneous spaces). We also express decreasing (G) as a monotone normality type condition and explore the preservation of decreasing (G) type properties under closed maps. The corresponding results for decreasing (A) spaces are unknown.
Definable completeness
Diagonals and discrete subsets of squares
In 2008 Juhász and Szentmiklóssy established that for every compact space there exists a discrete with . We generalize this result in two directions: the first one is to prove that the same holds for any Lindelöf -space and hence is -separable. We give an example of a countably compact space such that is not -separable. On the other hand, we show that for any Lindelöf -space there exists a discrete subset such that ; in particular, the diagonal is a retract of and the projection...
Dilating mappings, implicit functions and fixed point theorems in finite-dimensional spaces
Dimension inequalities for unions and mappings of separable metric spaces
Discontinuity points of exactly -to-one functions