On the -primitive
On theorems of Pu & Pu and Grande
Given a finite family of cliquish functions, , we can find a Lebesgue function such that is Darboux and quasi-continuous for every . This theorem is a generalization both of the theorem by H. W. Pu H. H. Pu and of the theorem by Z. Grande.
On uniform approximation of bounded approximately continuous functions by differences of lower semicontinuous and approximately continuous ones
On -continuous functions
Classes of functions continuous in various senses, in particular -continuous, -continuous, feeblz continuous a.o., and relations between the classes, are studied.
Points of continuity and quasicontinuity
Let C(f), Q(f), E(f) and A(f) be the sets of all continuity, quasicontinuity, upper and lower quasicontinuity and cliquishness points of a real function f: X → ℝ, respectively. The triplets (C(f),Q(f),A(f)), (C(f),E(f),A(f) and (Q(f),E(f),A(f)are characterized for functions defined on Baire metric spaces without isolated points.
Pointwise regularity associated with function spaces and multifractal analysis
The purpose of multifractal analysis of functions is to determine the Hausdorff dimensions of the sets of points where a function (or a distribution) f has a given pointwise regularity exponent H. This notion has many variants depending on the global hypotheses made on f; if f locally belongs to a Banach space E, then a family of pointwise regularity spaces are constructed, leading to a notion of pointwise regularity with respect to E; the case corresponds to the usual Hölder regularity, and...
Polynomial approximation and twenty years later.
Porosity, derived numbers and knot points of typical continuous functions
Possibly every real function is continuous on a non-meagre set.
Power-monotone sequences and Fourier series with positive coefficients.
Power-monotone sequences and Fourier series with positive coefficients.
Products of quasi-continuous functions
Products of simply continuous and quasicontinuous functions
Properties of connected functions in terms of their levels
Quantitative estimates of N.N. Luzin's C-property for classes of integrable functions
Quasicontinuity and some classes of Baire 1 functions
Quasiuniform limits of quasicontinuous functions
Quelques remarques sur la semi-continuité supérieure
Quotients of peripherally continuous functions
We characterize the family of quotients of peripherally continuous functions. Moreover, we study cardinal invariants related to quotients in the case of peripherally continuous functions and the complement of this family.
Ramsey, Lebesgue, and Marczewski sets and the Baire property
We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented. THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets. THEOREM. In the Ellentuck topology on , is a proper subset of the hereditary ideal associated with (s). We construct an example in the Ellentuck topology of a set which is...