Remarks on dimensions of Cartesian product sets

Chun Wei, Shengyou Wen, Zhixiong Wen

Given metric spaces $E$ and $F$, it is well known that $${\dim }_{H}E+{\dim }_{H}F\le {\dim }_H(E\times F)\le {\dim }_{H}E+{\dim }_{P}F,$$ $${\dim }_{H}E+{\dim }_{P}F\le {\dim }_P(E\times F)\le {\dim }_{P}E+{\dim }_{P}F,$$ an…