When the algebraic difference of two central Cantor sets is an interval?

Kód výsledku v IS VaVaI

RIV/67985840:_____/22:00569619 - isvavai.cz

Výsledek na webu

https://doi.org/10.54330/afm.126014

DOI - Digital Object Identifier

10.54330/afm.126014

Jazyk výsledku

angličtina

Název v původním jazyce

When the algebraic difference of two central Cantor sets is an interval?

Popis výsledku v původním jazyce

Let C(a),C(b) ⊂ [0, 1] be the central Cantor sets generated by sequences a, b ∈ (0, 1)N. The first main result of the paper gives a necessary and a sufficient condition for sequences a and b which inform when C(a)−C(b) is equal to [−1, 1] or is a finite union of closed intervals. One of the corollaries following from this results shows that the product of thicknesses of two central Cantor sets, the algebraic difference of which is an interval, may be arbitrarily small. We also show that there are sets C(a) and C(b) with the Hausdorff dimension equal to 0 such that their algebraic difference is an interval. Finally, we give a full characterization of the case, when C(a) − C(b) is equal to [−1, 1] or is a finite union of closed intervals.

Název v anglickém jazyce

When the algebraic difference of two central Cantor sets is an interval?

Popis výsledku anglicky

Let C(a),C(b) ⊂ [0, 1] be the central Cantor sets generated by sequences a, b ∈ (0, 1)N. The first main result of the paper gives a necessary and a sufficient condition for sequences a and b which inform when C(a)−C(b) is equal to [−1, 1] or is a finite union of closed intervals. One of the corollaries following from this results shows that the product of thicknesses of two central Cantor sets, the algebraic difference of which is an interval, may be arbitrarily small. We also show that there are sets C(a) and C(b) with the Hausdorff dimension equal to 0 such that their algebraic difference is an interval. Finally, we give a full characterization of the case, when C(a) − C(b) is equal to [−1, 1] or is a finite union of closed intervals.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

GF20-22230L: Banachovy prostory spojitých a lipschitzovských funkcí

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annales Fennici Mathematici

ISSN

2737-0690

e-ISSN

2737-114X

Svazek periodika

48

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

FI - Finská republika

Počet stran výsledku

23

Strana od-do

163-185

Kód UT WoS článku

000944143300009

EID výsledku v databázi Scopus

2-s2.0-85148584033