I wanted a closed nowhere dense subset of the Cantor space $\{0,1\}^\omega$.

I went with the set of all sequences where two consecutive terms repeat: $F=\{(x_0,x_0,x_1,x_1,x_2,x_2,\dots,x_n,x_n,\dots); (x_0,x_1,x_2,\dots,x_n,\dots)\in 2^\omega\}$.

Are there some other choices which look natural/standard?