O jednom úniku od spojitosti
Obecná teorie derivování funkcí a měr na katedře matematické analýzy MFF UK
On a generalization of the Darboux theorem to the multidimensional case.
On a problem of Mazur from "The Scottish Book" concerning second partial derivatives
We comment on a problem of Mazur from “The Scottish Book" concerning second partial derivatives. We prove that if a function f(x,y) of real variables defined on a rectangle has continuous derivative with respect to y and for almost all y the function has finite variation, then almost everywhere on the rectangle the partial derivative exists. We construct a separately twice differentiable function whose partial derivative is discontinuous with respect to the second variable on a set of positive...
On alternative functional equations. (Short Communication).
On an application of hypoellipticity to solutions of functional equations.
On Borel Classes of Sets of Fréchet Subdifferentiability
We study possible Borel classes of sets of Fréchet subdifferentiability of continuous functions on reflexive spaces.
On continuity and monotonicity of Darboux functions
On continuous interval functions
On Denjoy property and on approximate partial derivatives
On differentiability of Peano type functions
On differentiability of Peano type functions
On differentiability of Peano type functions. II
On essential cluster sets
On full derivatives
On functions satisfying a local Lipschitz condition of order α
On -differentiability and difference properties of functions
On ordinary differentiability of Bessel potentials
On points of absolute continuity. Functions of several variables
On sets of discontinuities of functions continuous on all lines
Answering a question asked by K. C. Ciesielski and T. Glatzer in 2013, we construct a -smooth function on and a closed set nowhere dense in such that there does not exist any linearly continuous function on (i.e., function continuous on all lines) which is discontinuous at each point of . We substantially use a recent full characterization of sets of discontinuity points of linearly continuous functions on proved by T. Banakh and O. Maslyuchenko in 2020. As an easy consequence of our...