Topologist's sine curve

In the branch of mathematics known as topology, the topologist's sine curve or Warsaw sine curve is a topological space with several interesting properties that make it an important textbook example.

It can be defined as the graph of the function ${\displaystyle \sin {\big (}{\frac {1}{x}}{\big )}}$ on the half-open interval ${\displaystyle (0,1]}$, together with the origin, under the topology induced from the Euclidean plane:

${\displaystyle T=\left\{\left(x,\sin {\tfrac {1}{x}}\right):x\in (0,1]\right\}\cup \{(0,0)\}.}$