Comb space

In mathematics, particularly topology, a comb space is a subspace of ${\displaystyle \mathbb {R} ^{2}}$ that looks rather like a comb. The comb space has some rather interesting properties and provides interesting counterexamples. The topologist's sine curve has similar properties to the comb space. The deleted comb space is an important variation on the comb space.

Consider ${\displaystyle \mathbb {R} ^{2}}$ with its standard topology and let K be the set ${\displaystyle \{1/n~|~n\in \mathbb {N} \setminus \{0\}\}}$. The set C defined by:

...
Wikipedia