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Mathematics > General Topology

Title: Endpoints of smooth plane dendroids

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.
Comments: 8 pages, 3 figures
Subjects: General Topology (math.GN)
MSC classes: 54F15, 54F45, 54F50
Cite as: arXiv:2405.01706 [math.GN]
  (or arXiv:2405.01706v1 [math.GN] for this version)

Submission history

From: David Sumner Lipham [view email]
[v1] Thu, 2 May 2024 20:04:57 GMT (528kb,D)

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