Totally disconnected semigroup compactifications of topological groups

Abstract We introduce the notion of an introverted Boolean algebra $\mathcal{B}$ closed-and-open subsets a topological group G, show that associated Stone space $(\nu_{\mathcal{B}} \nu_{\mathcal{B}})$ is totally disconnected semigroup compactification G and every takes this form. identify study universal compactification, semitopological G. Our main results are obtained independently Gelfand theory well-known properties (typically non-totally disconnected) compactifications GLUC, GW AP GAP, although we do employ to clarify relationship between these familiar their counterparts.