Deleted comb space
$(\{0\} \times \{0,1\}) \cup (\{\frac{1}{n}|n \in \mathbb{N}\} \times [0,1]) \cup ([0,1] \times \{0\})$ with the subspace topology of $\mathbb{R}^2$
$(\{0\} \times \{0,1\}) \cup (\{\frac{1}{n}|n \in \mathbb{N}\} \times [0,1]) \cup ([0,1] \times \{0\})$ with the subspace topology of $\mathbb{R}^2$