On oscillation of limit functions.
On Paracompactness and Almost Closed Mappings
On perfect mappings from to .
On piecewise-constant functions
On Preservation Of Normality.
On projectiveness in H-closed spaces
On pseudocompact, countably compact, locally bicompact mappings, and -mappings.
On quasi -open and quasi -closed functions.
On quasicontinuous and cliquish functions
On recurrent functions.
On -metrizable spaces
On semi -perfect functions.
On semi-homeomorphisms.
On sequence-covering --images of locally separable metric spaces
On sets of confluent and related mappings in the space
On smooth continua
On some separation axioms and -closure
On some subclasses of Darboux functions
On strongly preirresolute topological vector spaces
In the paper we obtain several characteristics of pre- of strongly preirresolute topological vector spaces and show that the extreme point of a convex subset of a strongly preirresolute topological vector space lies on the boundary.
On the closure of Baire classes under transfinite convergences
Let X be a Polish space and Y be a separable metric space. For a fixed ξ < ω₁, consider a family of Baire-ξ functions. Answering a question of Tomasz Natkaniec, we show that if for a function f: X → Y, the set is finite for every x ∈ X, then f itself is necessarily Baire-ξ. The proof is based on a characterization of sets which can be interesting in its own right.