References & Citations
Mathematics > General Topology
Title: Endpoints of smooth plane dendroids
(Submitted on 2 May 2024)
Abstract: We show that each endpoint of a smooth plane dendroid $X$ is accessible, and that the endpoint set $E(X)$ is circle-like in that every two of its points are separated by two other points. Also if $E(X)$ is totally disconnected and $1$-dimensional, then $X$ must contain an uncountable collection of pairwise-disjoint arcs. An example is constructed to show that this is false outside the plane.
Submission history
From: David Sumner Lipham [view email][v1] Thu, 2 May 2024 20:04:57 GMT (528kb,D)
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