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.
On the continuity and monotonicity of restrictions of connected functions
On the Graphs which are the Edge of a Plane Tiling.
On the hyperspaces of hereditarily indecomposable continua
On the inverse image of Baire spaces.
On the Maćkowiak-Tymchatyn theorem
On the maximum of generalized Darboux functions
On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor
We extend a theorem of S. Claytor in order to characterize the Peano generalized continua which are embeddable into the 2-sphere. We also give a characterization of the Peano generalized continua which admit closed embeddings in the Euclidean plane.
On the position of the set of monotone mappings in function spaces
On the preservation of Baire and weakly Baire category
We consider the question of preservation of Baire and weakly Baire category under images and preimages of certain kind of functions. It is known that Baire category is preserved under image of quasi-continuous feebly open surjections. In order to extend this result, we introduce a strictly larger class of quasi-continuous functions, i.e. the class of quasi-interior continuous functions. We show that Baire and weakly Baire categories are preserved under image of feebly open quasi-interior continuous...