{"paper":{"title":"Topological properties of inductive limits of closed towers of mertrizable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Saak Gabriyelyan","submitted_at":"2018-08-04T08:49:28Z","abstract_excerpt":"Let $\\{ G_n\\}_{n\\in\\w}$ be a closed tower of metrizable groups. Under a mild condition called $(GC)$ and which is strictly weaker than $PTA$ condition introduced in [22], we show that: (1) the inductive limit $G=\\mbox{g-}\\underrightarrow{\\lim}\\, G_n$ of the tower is a Hausdorff group, (2) every $G_n$ is a closed subgroup of $G$, (3) if $K$ is a compact subset of $G$, then $K\\subseteq G_m$ for some $m\\in\\omega$, (4) $G$ has a $\\mathfrak{G}$-base and countable tightness, (5) $G$ is an $\\aleph$-space, (6) $G$ is an Ascoli space if and only if either (i) there is $m\\in\\omega$ such that $G_n$ is op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01450","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"}