On strong spaceability of continuous functions and fractal dimensions

Jia Liu, Saisai Shi, Zhenliang Zhang

Given $s\in (1,2]$, define $$H_s[0,1]=\{f\in C[0,1]:{\dim }_H{G}_f([0,1])=s\}$$ and $${\overline{B}}_s[0,1]=\{f\in C[0,1]:{\overline{\dim }}_B{G}_f([0,1])=s\}.$$ The main goal of this paper i…