Regular Languages and Stone Duality*

Abstract. We give a new account of the relationships among varieties of regular languages, varieties of finite semigroups, and their characterization n terms of "implicit identities. " Our development, which is essentially topological in character, is based on the duality (established by Stone) between Boolean lgebras and certain topological spaces (which are now called "Stone spaces"). This duality does not seem to have been recognized in the literature on regular languages, even though it is well known that the regular languages over a fixed alphabet form a Boolean algebra nd that the "implicit operations " with a fixed number of operands form a Stone space. I