{"paper":{"title":"On topological properties of the formal power series substitution group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"I. Babenko, S. Bogatyi","submitted_at":"2009-12-09T17:35:13Z","abstract_excerpt":"Certain topological properties of the group $\\J(\\k)$ of all formal one-variable power series with coefficients in a topological unitary ring $\\k$ are considered. We show, in particular, that in the case when $\\k=\\Q$ the group $\\J(\\Q)$ has no continuous bijections into a locally compact group. In the case when $\\k=\\Z$ supplied with discrete topology, in spite of the fact that the group $\\J(\\Z)$ has continuous bijections into compact groups, it cannot be embedded into a locally compact group. In the final part of the paper the compression property for topological groups is considered. We establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1813","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}