We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
ARITHMETIC ON MORAN SETS.
- Authors
REN, XIAOMIN; TIAN, LI; ZHU, JIALI; JIANG, KAN
- Abstract
Let (ℳ , c k , n k) be a class of Moran sets. We assume that the convex hull of any E ∈ (ℳ , c k , n k) is [ 0 , 1 ]. Let A , B be two nonempty sets in ℝ. Suppose that f is a continuous function defined on an open set U ⊂ ℝ 2 . Denote the continuous image of f by f U (A , B) = { f (x , y) : (x , y) ∈ (A × B) ∩ U }. In this paper, we prove the following result. Let E 1 , E 2 ∈ (ℳ , c k , n k). Suppose that ∂ x f and ∂ y f are continuous if there exists some (x 0 , y 0) ∈ (E 1 × E 2) ∩ U such that sup k ≥ 1 { 1 − c k n k } < ∂ y f | (x 0 , y 0) ∂ x f | (x 0 , y 0) < inf k ≥ 1 c k 1 − n k c k , then f U (E 1 , E 2) contains an interior.
- Subjects
CONTINUOUS functions; TOPOLOGICAL spaces
- Publication
Fractals, 2019, Vol 27, Issue 8, pN.PAG
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X19501251