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Mathematics > General Topology

Title: Trees and Homogeneous LOTS

Abstract: We describe those complete linearly ordered topological spaces $X$ which are homogeneous (=CHLOTS). That is, $X$ is order isomorphic with any nonempty open interval in $X$. Using countable tail-like ordinals as indices, we build towers of distinct CHLOTS. Using tree constructions we are able to extend the towers and to describe an inductive procedure which yields every CHLOTS.
Subjects: General Topology (math.GN); Dynamical Systems (math.DS)
MSC classes: 54F05, 06A05, 05C05, 06F30
Cite as: arXiv:2107.13299 [math.GN]
  (or arXiv:2107.13299v2 [math.GN] for this version)

Submission history

From: Ethan Akin [view email]
[v1] Wed, 28 Jul 2021 11:45:34 GMT (137kb)
[v2] Tue, 21 Sep 2021 00:17:34 GMT (151kb)

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