Multiplication on uniform -Cantor sets
Let $ C $ be the middle-third Cantor set. Define $ C* C=\{x* y: x, y\in C\} $, where $*=+,-
,\cdot,\div $(when $*=\div $, we assume $ y\neq0 $). Steinhaus\cite {HS} proved in 1917 …
,\cdot,\div $(when $*=\div $, we assume $ y\neq0 $). Steinhaus\cite {HS} proved in 1917 …
Arithmetic on Moran sets
X Ren, L Tian, J Zhu, K Jiang - Fractals, 2019 - World Scientific
Let (ℳ, ck, nk) be a class of Moran sets. We assume that the convex hull of any E∈(ℳ, ck, nk)
is [0, 1]. Let A, B be two nonempty sets in ℝ. Suppose that f is a continuous function defined …
is [0, 1]. Let A, B be two nonempty sets in ℝ. Suppose that f is a continuous function defined …
Arithmetic Product Of Self-Similar Sets With Two Branches
Q Wang, K Zhang - Fractals, 2021 - World Scientific
For self-similar set E= λ 1 E∪(λ 2 E+ 1− λ 2)(λ 1+ λ 2< 1), we study the arithmetic product of
E and obtain that when λ 1≥ λ 2> 0 then E⋅ E=[0, 1] if and only if λ 1≥(1− λ 2) 2. To deal …
E and obtain that when λ 1≥ λ 2> 0 then E⋅ E=[0, 1] if and only if λ 1≥(1− λ 2) 2. To deal …