= Universal three-point space for product embeddings
{title2=$Y=(\{0,1,2\},\{\varnothing,\{2\},Y\})$}
Every <topological space>, including one without the <T0 space> property, embeds into a power of this three-point space. For each <open set> $U$, use a coordinate equal to $2$ on $U$ and $0$ elsewhere. Its <inverse image> of the only proper nonempty <open set> is $U$. For each point $a$, add a coordinate equal to $1$ at $a$ and $0$ elsewhere. These coordinates are continuous because the subspace $\{0,1\}$ has the <indiscrete topology>, and they separate all points. The combined diagonal map is <injective> and induces precisely the original <topology>, hence is a <topological embedding>.
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