The $S$-flat topology

For a commutative ring $R$ with unit $1\mathrm{\ne }0$ and a multiplicatively closed subset $S$ of $R$, we introduce a new topology on the $S$-prime spectrum ${\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}}_{S}R$ of $R$ called the $S$-flat topology. Our aims is to give an algebraic descriptions of the topological properties like compactness, irreducibility, connectivity and noetherianess with respect to this new topology .