On topological groups containing a Fr\'echet-Urysohn fan
Taras Banakh

TL;DR
This paper investigates the structure of topological groups containing a Frechet-Urysohn fan, showing that under certain normality and sequentiality conditions, such groups are either metrizable or have a specific product structure.
Contribution
It establishes conditions under which topological groups containing a Frechet-Urysohn fan are either metrizable or decomposable into a product of a $k_ ext{omega}$-space and a discrete space.
Findings
Closed metrizable subsets in such groups are locally compact.
Groups with a direct limit structure are either metrizable or a product of a $k_ ext{omega}$-space and a discrete space.
Abstract
Suppose G is a topological group containing a (closed) topological copy of the Frechet-Urysohn fan. If G is a perfectly normal sequential space (a normal k-space) then every closed metrizable subset in is locally compact. Applying this result to topological groups whose underlying topological space can be written as a direct limit of a sequence of closed metrizable subsets, we get that every such a group either is metrizable or is homeomorphic to the product of a -space and a discrete space.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology
