Qualitative cluster sets
Quasicontinuity and some classes of Baire 1 functions
Quelques remarques sur les classes de Baire des fonctions de deux variables
Quelques remarques sur les familles de fonctions de Baire de première classe
Ranks for baire multifunctions
Various ordinal ranks for Baire-1 real-valued functions, which have been used in the literature, are adapted to provide ranks for Baire-1 multifunctions. A new rank is also introduced which, roughly speaking, gives an estimate of how far a Baire-1 multifunction is from being upper semicontinuous.
Real functions having graphs connected and dense in the plane
Relative Differenzeneigenschaft
Remarks on Denjoy property and property of real functions
Remarks on density topology and its category analogue
Représentation des fonctions affines semi-continues inférieurement
Semiéquicontinuité approximative et measurabilité
Separate approximate continuity and strong approximate continuity
Separating sets by Darboux-like functions
We consider the following problem: Characterize the pairs ⟨A,B⟩ of subsets of ℝ which can be separated by a function from a given class, i.e., for which there exists a function f from that class such that f = 0 on A and f = 1 on B (the classical separation property) or f < 0 on A and f > 0 on B (a new separation property).
Sharkovskiĭ's theorem holds for some discontinuous functions
We show that the Sharkovskiĭ ordering of periods of a continuous real function is also valid for every function with connected graph. In particular, it is valid for every DB₁ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected graph.
Sierpiński's hierarchy and locally Lipschitz functions
Let Z be an uncountable Polish space. It is a classical result that if I ⊆ ℝ is any interval (proper or not), f: I → ℝ and then f ○ g ∈ for every if and only if f is continuous on I, where stands for the αth class in Baire’s classification of Borel measurable functions. We shall prove that for the classes in Sierpiński’s classification of Borel measurable functions the analogous result holds where the condition that f is continuous is replaced by the condition that f is locally Lipschitz...
Some generalizations of the notion of continuity and Denjoy property of functions
Some properties of a function connected to a double series.
Some results on projection of planar sets
In this paper we define certain types of projections of planar sets and study some properties of such projections.
Space of Baire functions. I
Several equivalent conditions are given for the existence of real-valued Baire functions of all classes on a type of -analytic spaces, called disjoint analytic spaces, and on all pseudocompact spaces. The sequential stability index for the Banach space of bounded continuous real-valued functions on these spaces is shown to be either , or (the first uncountable ordinal). In contrast, the space of bounded real-valued Baire functions of class 1 is shown to contain closed linear subspaces with index...
Stability in the -norm and -norm of classes of Lipschitz functions of one variable.