topologist's sine curve

The topologist's sine curve has similar properties to the comb space.

Two variants of the topologist's sine curve have other interesting properties.

This is a compact subset of the plane produced by "closing up" a topologist's sine curve with an arc.

The topologist's sine curve T is connected but neither locally connected nor path connected.

The topologist's sine curve is a subspace of the Euclidean plane which is connected, but not locally connected.

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

The closed topologist's sine curve can be defined by taking the topologist's sine curve and adding its set of limit points, .

Moreover, the path components of the topologist's sine curve C are U, which is open but not closed, and , which is closed but not open.