# Is $\mathsf{DSPACE}(n)=\mathsf{DSPACE}(n/\log\log n)$?

We know that $$\mathsf{DSPACE}(\log\log n) = \mathsf{DSPACE}(1)$$ according to this proof. Can we claim that $$\mathsf{DSPACE}(n)=\mathsf{DSPACE}(n/\log\log n)$$ or something like $$\mathsf{DSPACE}(n^3)=\mathsf{DSPACE}(n^3/(\log\log n)^k)$$ for some $$k\in \mathbb{N}$$?