Let $X$ be an equidimensional scheme satisfying the properties $P_1,\ldots,P_n$. Could someone please give me an example (with a reference or proof) of $P_1,\ldots, P_n$ such that the following statement is true?
Every open affine subscheme of $X$ is equidimensional
I am mainly interested in the case where $X$ is neither irreducible nor reduced.