Journal of Lie Theory

no. 1
Continuity Characterizing Totally Disconnected Locally Compact Groups
Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 1-7
For a locally compact group G and its compact space SUB(G) of closed subgroups let μG: 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.
DOI: 10.5802/jolt.824
Classification: 22D05, 22C05, 54B20
Keywords: Locally compact group, Chabauty space, hyperspace of closed subgroups, continuity, monothetic subgroup 
@article{JOLT_2015_25_1_a0,
     author = {K. H. Hofmann and G. A. Willis},
     title = {Continuity {Characterizing} {Totally} {Disconnected} {Locally} {Compact} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {1--7},
     year = {2015},
     volume = {25},
     number = {1},
     doi = {10.5802/jolt.824},
     zbl = {1317.22004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.824/}
}
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K. H. Hofmann; G. A. Willis. Continuity Characterizing Totally Disconnected Locally Compact Groups. Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 1-7. doi: 10.5802/jolt.824

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