Cones of Lower Semicontinuous Functions and a Characterisation of Finely Hyperharmonic Functions.
Connected simple graphs and a selection problem
Connectivity of diagonal products of Baire one functions
We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.
Connectivity points and Darboux points of real functions
Continuous-, derivative-, and differentiable-restrictions of measurable functions
We review the known facts and establish some new results concerning continuous-restrictions, derivative-restrictions, and differentiable-restrictions of Lebesgue measurable, universally measurable, and Marczewski measurable functions, as well as functions which have the Baire properties in the wide and restricted senses. We also discuss some known examples and present a number of new examples to show that the theorems are sharp.
Countable decomposition of derivatives and Baire 1 functions.
Density Continuity versus Continuity.
Deux exemples de fonctions non mesurables
Die Elemente der Functionenlehre.
Discontinuity points of exactly -to-one functions
Eine Äquivalenzrelation in der Kategorie der Phasenfunktionen
Eine Bermerkung über Stammfunktion und Zwischenwerteigenschaft.
Einiges über Functionen mit nicht-abzahlbaren Unstetigkeitsstellen
Finitely generated semigroups of continuous on [0,1]
Fractional Iteration and a Generalised Abel's Equation in Two Variables
Function decompositions related to the Luzin N-property.
Functions characterized by images of sets
For non-empty topological spaces X and Y and arbitrary families ⊆ and we put =f ∈ : (∀ A ∈ )(f[A] ∈ . We examine which classes of functions ⊆ can be represented as . We are mainly interested in the case when is the class of all continuous functions from X into Y. We prove that for a non-discrete Tikhonov space X the class (X,ℝ) is not equal to for any ⊆ and ⊆ (ℝ). Thus, (X,ℝ) cannot be characterized by images of sets. We also show that none of the following classes of...
Generalized distributivity for real, continuous functions. II: Local solutions in the continuous case.
Grundlagen für eine Theorie der Functionen einer veränderlichen rellen Grösse [Book]
How smooth is almost every function in a Sobolev space?
We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.