
Journal of Lie Theory 25 (2015), No. 1, 001007 Copyright Heldermann Verlag 2015 Continuity Characterizing Totally Disconnected Locally Compact Groups Karl H. Hofmann Fachbereich Mathematik, Technische Universität, Schlossgartenstr. 7, 64289 Darmstadt, Germany hofmann@mathematik.tudarmstadt.de George A. Willis School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia george.willis@newcastle.edu.au For a locally compact group G and its compact space SUB(G) of closed subgroups let μ_{G}: G > SUB(G) denote the function which attaches to an element g of G the closed subgroup generated by it. It is shown that G is totally disconnected if and only if μ is continuous. Several other functions which associate with an element of G in a natural way a closed subgroup of G are discussed with respect to their continuity in totally disconnected locally compact groups. Keywords: Locally compact group, Chabauty space, hyperspace of closed subgroups, continuity, monothetic subgroup. MSC: 22D05, 22C05, 54B20 [ Fulltextpdf (244 KB)] for subscribers only. 