Real computation with least discrete advice: A complexity theory of nonuniform computability with applications to effective linear algebra
M Ziegler - Annals of Pure and Applied Logic, 2012 - Elsevier
It is folklore particularly in numerical and computer sciences that, instead of solving some
general problem f: X∋ x↦ f (x)∈ Y, additional structural information about the input x∈ X (eg …
general problem f: X∋ x↦ f (x)∈ Y, additional structural information about the input x∈ X (eg …
[PDF][PDF] Path continuity connected with density and porosity
S Kowalczyk, M Turowska - Modern Real Analysis;, 2015 - dspace.uni.lodz.pl
The notion of path continuity appeared in the theory of real functions at the beginning of
XXth century. Path continuity means that at every x∈ R a family Bx of subsets of R,„big” in …
XXth century. Path continuity means that at every x∈ R a family Bx of subsets of R,„big” in …
[PDF][PDF] On additive countably continuous functions
T Natkaniec - Publ. Math. Debrecen, 2011 - scholar.archive.org
We construct an example of additive Darboux function f: R→ R which is strongly countably
continuous and discontinuous. We show also that if an additive function f is covered by …
continuous and discontinuous. We show also that if an additive function f is covered by …
[PDF][PDF] Path continuity connected with the notion of density
S Kowalczyk, K Nowakowska - … and present-day topics in real …, 2013 - dspace.uni.lodz.pl
AM Bruckner, RJ O'Malley and BS Thomson in [4] investigated the notion of a system of
paths and studied a number of generalized derivatives. Properties of path continuous …
paths and studied a number of generalized derivatives. Properties of path continuous …
Finitely continuous Darboux functions
M Kowalewski, M Marciniak - Quaestiones Mathematicae, 2021 - Taylor & Francis
In this paper we consider properties of the class of finitely continuous Darboux functions. In
particular, we study some properties of the set of discontinuity points of the function from this …
particular, we study some properties of the set of discontinuity points of the function from this …
[PDF][PDF] On Extension Problem, Decomposing and Covering of Functions
Z Grande, M Marciniak - Filipczak M., Wagner-Bojakowska E.(red …, 2013 - dspace.uni.lodz.pl
If (X, T) is a topological normal space, then by well known Tietze extension theorem, for each
nonempty closed set A⊂ X and every continuous function g: A→[0, 1] there is a continuous …
nonempty closed set A⊂ X and every continuous function g: A→[0, 1] there is a continuous …