Definition:Sierpiński Space

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Definition

The Sierpiński space is a particular point space with exactly two elements.

Its usual presentation is:

$T = \left({\left\{{0, 1}\right\}, \left\{{\varnothing, \left\{{0}\right\}, \left\{{0, 1}\right\}}\right\}}\right)$

that is, as a particular point topology on the set $\left\{{0, 1}\right\}$ where the particular point is $0$.


It can also immediately be seen to be an excluded point topology on the set $\left\{{0, 1}\right\}$ where the excluded point is $1$.


The Sierpiński space is considered to be a trivial instance of both the particular point topology and the excluded point topology.


Source of Name

This entry was named for Wacław Franciszek Sierpiński.


Also see

  • Results about the Sierpiński space can be found here.


Sources