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 sin(1/x) on the half-open interval (0, 1], together with the origin, under the topology induced from the Euclidean plane:

    T

    =



      {





          (



            x

            ,

            sin

            ⁡







                  1

                  x









          )



        :

        x

        ∈

        (

        0

        ,

        1

        ]



      }



    ∪

    {

    (

    0

    ,

    0

    )

    }

    .

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