On quasi-continuous iteration semigroups and groups of real functions
On quasi-uniform convergence of a sequence of s.q.c. functions
On representations of Baire functions in a given family as sums of Baire Darboux functions with a common summand
On sequences of real functions with the Darboux property
On sets of points of semicontinuity in fine topologies generated by an ideal
On similarity between topologies
Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.
On some alternative functional equations. (Short Communication).
On some properties of Hamel bases and their applications to Marczewski measurable functions
We introduce new properties of Hamel bases. We show that it is consistent with ZFC that such Hamel bases exist. Under the assumption that there exists a Hamel basis with one of these properties we construct a discontinuous and additive function that is Marczewski measurable. Moreover, we show that such a function can additionally have the intermediate value property (and even be an extendable function). Finally, we examine sums and limits of such functions.
On some properties of Hamel bases connected with the continuity of polynomial functions.
On some properties of J-convex stochastic processes.
On some properties of the spaces of almost continuous functions.
On some shift invariant integral operators, univariate case
In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and...
On some subclasses of Darboux functions
On spaces with the ideal convergence property
Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.
On sums of Darboux functions
On the -continuity of real function. II.
On the almost monotone convergence of sequences of continuous functions
A sequence (f n)n of functions f n: X → ℝ almost decreases (increases) to a function f: X → ℝ if it pointwise converges to f and for each point x ∈ X there is a positive integer n(x) such that f n+1(x) ≤ f n (x) (f n+1(x) ≥ f n(x)) for n ≥ n(x). In this article I investigate this convergence in some families of continuous functions.
On the asymptotic behaviour of a modulus of continuity with discrete description
On the behaviour of continuous real functions in the neighbourhood of a fixed point.
On the characterization of quasiarithmetic means with weight function.