Category:Sierpiński Space

This category contains results about the Sierpiński space.

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

Its usual presentation is:

$T = \struct {\set {0, 1}, \set {\O, \set 0, \set {0, 1} } }$

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

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