Prove that the set $\displaystyle T = \{(x,y) \in I \times I : x<y\} $ is a connected subset of $\displaystyle \Re^2$ with the standard topology.

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- Feb 24th 2009, 10:15 AMAmanda1990Darboux Theorem
Prove that the set $\displaystyle T = \{(x,y) \in I \times I : x<y\} $ is a connected subset of $\displaystyle \Re^2$ with the standard topology.

- Feb 25th 2009, 02:25 PMHenryB
Just note that T is path connected (easy proof) and so connected.