On generalized Darboux and connectivity functions
On Grande’s problem concerning functions
On jumping functions by connected sets
On Köpcke and Pompeiu functions
On level sets of Darboux functions
On limit numbers of real functions
On Mauldin's classification of real functions
On more general Lipschitz spaces.
On nowhere density of the class of somewhat continuous functions in
On nowhere weakly symmetric functions and functions with two-element range
A function f: ℝ → {0,1} is weakly symmetric (resp. weakly symmetrically continuous) at x ∈ ℝ provided there is a sequence hₙ → 0 such that f(x+hₙ) = f(x-hₙ) = f(x) (resp. f(x+hₙ) = f(x-hₙ)) for every n. We characterize the sets S(f) of all points at which f fails to be weakly symmetrically continuous and show that f must be weakly symmetric at some x ∈ ℝ∖S(f). In particular, there is no f: ℝ → {0,1} which is nowhere weakly symmetric. It is also shown that if at each point x we...
On Pawlak's problem concerning entropy of almost continuous functions
We prove that if f: → is Darboux and has a point of prime period different from , i = 0,1,..., then the entropy of f is positive. On the other hand, for every set A ⊂ ℕ with 1 ∈ A there is an almost continuous (in the sense of Stallings) function f: → with positive entropy for which the set Per(f) of prime periods of all periodic points is equal to A.
On points of absolute continuity, III
On points of qualitative semicontinuity
On pointwise limits of sequences of -continuous functions
On quasicontinuous and cliquish functions
On quasi-continuous bijections.
On quasi-continuous functions having Darboux property.
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