A compact set E⊂ R d is said to be arithmetically thick if there exists a positive integer n so
that the n‐fold arithmetic sum of E has non‐empty interior. We prove the arithmetic thickness …

Let C 1 and C 2 be two Cantor sets in R. Suppose that the size of the largest gap of C 1 is
not greater than the diameter of C 2, and vice versa. Newhouse (Hyperbolicity and sensitive …

We extend some approach to the family of symmetric means (ie symmetric functions M:⋃ n=
1∞ I n→ I with min≤ M≤ max; I is an interval). Namely, it is known that every symmetric …

We prove that for two connected sets with cardinalities greater than, if one of E and F is
compact and not a line segment, then the arithmetic sum has nonempty interior. This …

Let $ C_1 $ and $ C_2 $ be two Cantor sets with convex hull $[0, 1] $. Newhouse proved if
$\tau (C_1)\cdot\tau (C_2)\geq 1$, then the arithmetic sum $ C_1+ C_2 $ is an interval …

We answer a question of Banakh, Jabłońska and Jabłoński by showing that for $ d\geqslant
2$ there exists a compact set $ K\subseteq\mathbb {R}^ d $ such that the projection of K …

On the Arithmetic Sums of Fractal Sets in Rd Page 1 On the Arithmetic Sums of Fractal Sets in
Rd WU, Yufeng A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of …