Matematická súťaž vysokoškolákov 1986
On approximation of Baire functions by Darboux functions
A necessary and sufficient condition for continuity of additive functions
Za profesorom Neubrunnom
Characteristic Types of Convergence for Certain Classes of Darboux-Baire 1 Functions
Some Characterizations of the Darboux Continuity of Real Functions
Iterates of piecewise monotonic continuous functions
On measures connected with the Cauchy equation.
On measures connected with the Cauchy equation. (Short Communication).
K životnému jubileu profesora Neubrunna
K šesťdesiatke profesora Tibora Šaláta
A theorem of Šarkovskii characterizing continuous maps of zero topological entropy
On a generalized Dhombres functional equation. II.
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a previous paper we proved that no continuous solution can cross the line where is a fixed point of , with a possible exception for . The range of any non-constant continuous solution is an interval whose end-points are fixed by and which contains in its interior no fixed point except for . We also gave a characterization of the class of continuous...
ω-Limit sets for triangular mappings
In 1992 Agronsky and Ceder proved that any finite collection of non-degenerate Peano continua in the unit square is an ω-limit set for a continuous map. We improve this result by showing that it is valid, with natural restrictions, for the triangular maps (x,y) ↦ (f(x),g(x,y)) of the square. For example, we show that a non-trivial Peano continuum C ⊂ I² is an orbit-enclosing ω-limit set of a triangular map if and only if it has a projection property. If C is a finite union of Peano continua then,...
On certain properties characterizing locally separable metric spaces
The structure of -limit sets for continuous maps of the interval
We prove that every infinite nowhere dense compact subset of the interval is an -limit set of homoclinic type for a continuous function from to .
The continuous solutions of a generalized Dhombres functional equation
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a series of papers by P. Kahlig and J. Smítal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under and which contains in its interior no fixed point except for . They also provide a characterization of the class of monotone solutions and prove a necessary and sufficient condition for any solution...
The converse problem for a generalized Dhombres functional equation
We consider the functional equation where is a given homeomorphism of an open interval and is an unknown continuous function. A characterization of the class of continuous solutions is given in a series of papers by Kahlig and Smítal 1998–2002, and in a recent paper by Reich et al. 2004, in the case when is increasing. In the present paper we solve the converse problem, for which continuous maps , where is an interval, there is an increasing homeomorphism of such that . We...
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