 Sierpiński space

The Sierpiński space is $\{0,1\}$ with open sets $\varnothing$, $\{1\}$, and $\{0,1\}$. Continuous maps $X\to S$ are in bijection with open subsets of $X$ through $g\mapsto g^{-1}(1)$.

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.