Geometric Picture of Open Subsets of Irreducible spaces in Zariski topology

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I understand why nonempty open subsets of irreducible topological spaces are dense. I am having trouble comprehending how this translates to Zariski's topology. We know that a finite affine variety is irreducible iff it is a single point. How do you take an open subset of a single point? What does this look like geometrically?