On the continuity and monotonicity of restrictions of connected functions
On the convergence of -primitives
On the existence of -primitives on arbitrary metric spaces
On the fixed points in an -limit set
Let and be closed subsets of [0,1] with a subset of the limit points of . Necessary and sufficient conditions are found for the existence of a continuous function such that is an -limit set for and is the set of fixed points of in .
On the functionally countable subalgebra of C(X)
On the generalized property
On the ideal convergence of sequences of quasi-continuous functions
For any Borel ideal ℐ we describe the ℐ-Baire system generated by the family of quasi-continuous real-valued functions. We characterize the Borel ideals ℐ for which the ideal and ordinary Baire systems coincide.
On the insertion of Darboux functions
The main goal of this paper is to characterize the family of all functions f which satisfy the following condition: whenever g is a Darboux function and f < g on ℝ there is a Darboux function h such that f < h < g on ℝ.
On the mappings and in intermediate rings of
In this article, we investigate new topological descriptions for two well-known mappings and defined on intermediate rings of . Using this, coincidence of each two classes of -ideals, -ideals and -ideals of is studied. Moreover, we answer five questions concerning the mapping raised in [J. Sack, S. Watson, and among intermediate rings, Topology Proc. 43 (2014), 69–82].
On the maximum and the minimum of quasi-continuous functions
On the maximum of generalized Darboux functions
On the pointwise limits of sequences of Świątkowski functions
The characterization of the pointwise limits of the sequences of Świątkowski functions is given. Modifications of Świątkowski property with respect to different topologies finer than the Euclidean topology are discussed.
On the theorems of Y. Mibu and G. Debs on separate continuity.
On the -primitive
On topological properties of the spaces of Darboux Baire 1 functions and bounded derivatives
We investigate the topological structure of the space 𝓓ℬ₁ of bounded Darboux Baire 1 functions on [0,1] with the metric of uniform convergence and with the p*-topology. We also investigate some properties of the set Δ of bounded derivatives.
On uniform approximation of bounded approximately continuous functions by differences of lower semicontinuous and approximately continuous ones
On -embedded sets and extension of mappings
We introduce and study -embedded sets and apply them to generalize the Kuratowski Extension Theorem.
Order extension of order monomorphisms on a preordered topological space.
Ordinal remainders of classical ψ-spaces
Let ω denote the set of natural numbers. We prove: for every mod-finite ascending chain of infinite subsets of ω, there exists , an infinite maximal almost disjoint family (MADF) of infinite subsets of the natural numbers, such that the Stone-Čech remainder βψ∖ψ of the associated ψ-space, ψ = ψ(ω,ℳ ), is homeomorphic to λ + 1 with the order topology. We also prove that for every λ < ⁺, where is the tower number, there exists a mod-finite ascending chain , hence a ψ-space with Stone-Čech remainder...
Oscillations, quasi-oscillations and joint continuity.