Is the Closed Unit Square Homeomorphic to the Closed Unit Disc?

[metder]

I realize this is a classic problem, but I'm not sure exactly how to start on it:
Show that the closed unit square region is homeomorphic to the closed unit disc.

 

[lavinia]

I realize this is a classic problem, but I'm not sure exactly how to start on it:
Show that the closed unit square region is homeomorphic to the closed unit disc.

Draw a picture and I think you will immediately see the mapping

 

[mathwonk]

I think Lavinia is suggesting you start by showing a single circle is homeomorphic to a single square, and then apply that to a family of expanding circles and squares filling up the regions.

 

[lavinia]

I think Lavinia is suggesting you start by showing a single circle is homeomorphic to a single square, and then apply that to a family of expanding circles and squares filling up the regions.

yes. And I think this can be done with a simple function