{"paper":{"title":"Connected neighborhoods in Cartesian products of solenoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GN","authors_text":"Alejandro Illanes, Emanuel R. M\\'arquez, Jan P. Boro\\'nski","submitted_at":"2018-12-06T11:51:21Z","abstract_excerpt":"Given a collection of pairwise co-prime integers $% m_{1},\\ldots ,m_{r}$, greater than $1$, we consider the product $\\Sigma =\\Sigma _{m_{1}}\\times \\cdots \\times \\Sigma _{m_{r}}$, where each $\\Sigma _{m_{i}}$ is the $m_{i}$-adic solenoid. Answering a question of D. P. Bellamy and J. M. \\L ysko, in this paper we prove that if $M$ is a subcontinuum of $\\Sigma $ such that the projections of $M$ on each $\\Sigma _{m_{i}}$ are onto, then for each open subset $U$ in $\\Sigma $ with $M\\subset U$, there exists an open connected subset $V$ of $\\Sigma $ such that $M\\subset V\\subset U$; i.e. any such $M$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02480","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"}