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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00569619" target="_blank" >RIV/67985840:_____/22:00569619 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.54330/afm.126014" target="_blank" >https://doi.org/10.54330/afm.126014</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.54330/afm.126014" target="_blank" >10.54330/afm.126014</a>

Result language
angličtina
Original language name
When the algebraic difference of two central Cantor sets is an interval?
Original language description
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.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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