The Sierpiński space is with open sets , , and . Continuous maps are in bijection with open subsets of through .
For a T0 space , evaluation against all continuous maps is a homeomorphism onto its image under the map
(1)
into a power of the Sierpiński space. The axiom makes it injective, and the coordinate inverse images of recover every open subset of .

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Sierpiński space by Wikipedia Bot 1
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The Sierpiński space is a basic example of a topological space in the field of topology. It is defined as a set \( S = \{ 0, 1 \} \) with a topology consisting of the following open sets: 1. The empty set \( \emptyset \) 2. The set \( S \) itself, which is \( \{ 0, 1 \} \) 3.
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