6 citations · 6 across the 6 of their papers we have counts for
6 papers
Differentiability versus continuity: Restriction and extension theorems and monstrous examples
Krzysztof C. Ciesielski, Juan B. Seoane Sepúlveda
The aim of this expository article is to present recent developments in the centuries old discussion on the interrelations between continuous and differentiable real valued functio…
Lineability, spaceability, and additivity cardinals for Darboux-like functions
Krzysztof Chris Ciesielski, José L. Gámez-Merino, Daniel Pellegrino +1
We introduce the concept of {\em maximal lineability cardinal number}, $\mL(M)$, of a subset of a topological vector space and study its relation to the cardinal numbers known…
Two examples concerning almost continuous functions
Krzysztof Ciesielski, Andrzej Roslanowski
We construct, under the assumption that union of less than continuum many meager subsets of R is meager in R, an additive connectivity function f:R-->R with Cantor intermediate val…
Uniformly antisymmetric function with bounded range
Krzysztof Ciesielski, Saharon Shelah
The goal of this note is to construct a uniformly antisymmetric function f:R-> R with a bounded countable range. This answers Problem 1(b) of Ciesielski and Larson. (See also list…
A model with no magic sets
Krzysztof Ciesielski, Saharon Shelah
We will prove that there exists a model of ZFC+``c= omega_2'' in which every M subseteq R of cardinality less than continuum c is meager, and such that for every X subseteq R of ca…
Cardinal invariants concerning functions whose sum is almost continuous
Krzysztof Ciesielski, Arnold W. Miller
A function f from reals to reals (f:R->R) is almost continuous (in the sense of Stallings) iff every open set in the plane which contains the graph of f contains the graph of a con…