Editing Topologist's sine curve (section)

{{Short description|Pathological topological space}}
[[Image:Topologist's sine curve.svg|420px|thumb| As ''x'' approaches zero from the right, the magnitude of the rate of change of 1/''x'' increases. This is why the frequency of the sine wave increases as one moves to the left in the graph.]]

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 a function|graph]] of the function sin(1/''x'') on the [[half-open interval]] (0,&nbsp;1], together with the origin, under the topology [[subspace topology|induced]] from the [[Euclidean plane]]:

:<math> T = \left\{  \left( x, \sin \tfrac{1}{x}  \right ) :  x \in (0,1] \right\} \cup \{(0,0)\}. </math>