  For a commutative ring $R$ with unit $1\ne 0$ and a multiplicatively closed
subset $S$ of $R$, we introduce a new topology on the $S$-prime spectrum
$\mathrm{Spec}_SR$ 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 .
