# Category:Sierpiński Space

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This category contains results about the Sierpiński space.

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

Its usual presentation is:

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

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.

## Pages in category "Sierpiński Space"

The following 9 pages are in this category, out of 9 total.