Let $X$ be a topological space. $X$ is connected if $X\neq U\cup V$ with open sets $U,V$ and $U\cap V=\emptyset$.
If you consider $A:=(0,1]\cup(2,3)\subset\mathbb R$, $A$ is not connected.
But how can you prove it? Clearly I have to find those open sets like above but how? Thanks!