Are $[0,1)\times [0,1)$ and $[0,1]\times [0,1)$ homeomorphic?   Not getting any idea how to start.
Show that $[0, 1)\times[0, 1)$ is homeomorphic to $[0, 1]\times[0, 1)$ but not to $[0, 1]\times[0, 1]$. When I sketch these spaces it this statement makes sense intuitively because $[0, 1]\times[0, 1]$ is closed and $[0, 1)\times[0, 1)$ and $[0, 1]\times[0, 1)$ are each "missing" part of their boundary which would make them closed. I also know, $[0, 1]\times[0, 1]$ is compact and compact spaces are not homeomorphic to non-compact spaces.   I am having trouble saying this explicitly, as is pretty obvious in the clumsiness of the wording above.
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