Results 71 to 80 of about 122,847 (179)

All projections of a typical Cantor set are Cantor sets

Topology and its Applications, 2020
In 1994, John Cobb asked: given $N>m>k>0$, does there exist a Cantor set in $\mathbb R^N$ such that each of its projections into $m$-planes is exactly $k$-dimensional? Such sets were described for $(N,m,k)=(2,1,1)$ by L.Antoine (1924) and for $(N,m,m)$ by K.Borsuk (1947). Examples were constructed for the cases $(3,2,1)$ by J.Cobb (1994), for $
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Sums of powers, and products of elements of the middle third Cantor set

, 2020
Consider the set of sums of $m$'th powers of elements belonging to the Cantor middle third set $\mathscr{C}$, and the question of the number of terms required to ensure we find a large open interval in this set. Also consider the question of finding open
Pathak, Aritro
core  

Minimal Cantor sets

, 2023
A Cantor set is a topological space which admits a hierarchy of clopen covers. A minimal Cantor set is a Cantor set together with a map such that every orbit is dense in the Cantor set. In this thesis we us inverse limits to study minimal Cantor sets and their properties.
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Lebesgue Constants for Cantor Sets

Experimental Mathematics
We evaluate the values of the Lebesgue constants in polynomial interpolation for three types of Cantor sets. In all cases, the sequences of Lebesgue constants are not bounded. This disproves the statement by Mergelyan.
Alexander Goncharov, Yaman Paksoy
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Twofold Cantor sets in R

Sibirskie Elektronnye Matematicheskie Izvestiya, 2018
We introduce a class of self-similar sets which we call {\em twofold Cantor sets} $K_{pq}$ in $\mathbb R$ which are totally disconnected, do not have weak separation property and at the same time have isomorphic self-similar structures.
Kamalutdinov, K. G., Tetenov, A. V.
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Connected metrizable subtopologies and partitions into copies of the Cantor set

Applied General Topology, 2006
We prove under Martin’s Axiom that every separable metrizable space represented as the union of less than 2 ω zero-dimensional compact subsets is zero-dimensional. On the other hand, we show in ZFC that every separable completely metrizable space without
Irina Druzhinina
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A family of Cantorvals

Open Mathematics, 2019
The set of subsums of the series ∑n=1∞$\begin{array}{} \sum_{n=1}^{\infty} \end{array}$ xn is known to be one of three types: a finite union of intervals, homeomorphic to the Cantor set, or of the type known as a Cantorval.
Ferdinands John, Ferdinands Timothy
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Dynamical System on Cantor Set

Tokyo Journal of Mathematics, 1998
This paper is devoted to the Cantor sets generated by piecewise \(C^{1+\gamma}\) transformations \((\gamma> 0)\). Here, the author considers only Markov cases. Non-Markov cases will be treated in forthcoming paper. The author describes dynamical systems on Cantor set using in particular symbolic approach.
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Characterization of the macro-Cantor set up to coarse equivalence

Karpatsʹkì Matematičnì Publìkacìï, 2010
We characterize metric spaces that are coarsely equivalent to themacro-Cantor set $2^{
Zarichnyi I.M.
doaj  

Non-local Integrals and Derivatives on Fractal Sets with Applications

Open Physics, 2016
In this paper, we discuss non-local derivatives on fractal Cantor sets. The scaling properties are given for both local and non-local fractal derivatives. The local and non-local fractal differential equations are solved and compared.
Golmankhaneh Alireza K., Baleanu D.
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