Is there a continuous bijection between an interval and a square: $[0=?iso-8859-1?Q?=2C1]_\mapsto_[0=2C1]_\times_[0=2C1]$=3F_=96_math.stackexc?=hange.com

Is there a continuous bijection between an interval and a square: $[0,1]
\mapsto [0,1] \times [0,1]$? – math.stackexchange.com

Is there a continuous bijection from $[0,1]$ onto $[0,1] \times [0,1]$?
That is with $I=[0,1]$ and $S=[0,1] \times [0,1]$, is there a continuous
bijection $$ f: I \to S? $$ I know there is a ...