Consider the unit ball [itex]B:=B_1(0)\subset \mathbb{R}^2[/itex]. How can one prove that the set [itex]B\times B \setminus D[/itex], where [itex]D:=\left\{(x, x)\biggr| x \in B\right\}[/itex] is the diagonal, is non-contractible? Is it even disconnected? Thank you in advance.(adsbygoogle = window.adsbygoogle || []).push({});

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# Non-contractibility of a set

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