<P> In mathematics, an F set (said F - sigma set) is a countable union of closed sets . The notation originated in France with F for fermé (French: closed) and σ for somme (French: sum, union). </P> <P> In metrizable spaces, every open set is an F set . The complement of an F set is a G set . In a metrizable space, any closed set is a G set . </P>

Show that each open set is an f sigma set