Corners of Hilbert cube
The space $\{(a_i)_{i \in \mathbb{N}}|a_i \in \{0,1\}\}$ with distance $ d(a,b)=\left(\sum_{i=0}^\infty \frac{(a_i-b_i)^2}{2^{2n}}\right)^{\frac 12}$
The space $\{(a_i)_{i \in \mathbb{N}}|a_i \in \{0,1\}\}$ with distance $ d(a,b)=\left(\sum_{i=0}^\infty \frac{(a_i-b_i)^2}{2^{2n}}\right)^{\frac 12}$