I need a little help with "Consider $B\subset\Re^{n}$ a ball (open or closed). Show that for all $x\in B$, the set $B-\{x\}$ is connected". First of all, i know that every ball (open or closed) is connected in $\Re^{n}$. I was thinking in proof by contrapositive.
2026-03-25 18:08:26.1774462106
Consider $B\subset\Re^{n}$ a ball (open or closed). Show that for all $x\in B$, the set $B-\{x\}$ is connected.
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IT is very easy to join any two points in the punctured ball with a path. Therefore this set has one path (and therefore connected) component.