COMPLEMENTARY TOPOLOGY AND BOOLEAN RING

Abstract

A topology $\tau$ on a set $X$ is called Complementary topology if for each open set $U$ in-$\tau$, its Complement $X-U$ is also in $\tau$. Since Complementary topologies are the only topologies that form a Boolean ring under the usual operations. These topologies are characterized. The paper then concentrates on the determination of the ideals and maximal ideals of such a ring.