I want to show that a map from the cantor set $C$ to its product $C\times C$ is homeomorphic, and I am stuck at continuity because in the epsilon delta proof I am not sure how to deal with the absolute values in the range.
How is the absolute value $|(x,y)|$ defined if $(x,y)$ is an element of a product space, say $[0,1]$x$[0,1]$?
Should I treat this like a vector and just take a Euclidean distance? My topology background is very limited, thanks.