On compact subsets of the reals
General Topology
2023-12-21 v1
Abstract
Motivated by results of J. R. Kline and R. L. Moore (1919) that a compact subset of the plane, homeomorphic to a subset of the reals, lies on the arc, we give a purely topological characterisation of compact sets of the reals. This allows us to reduce investigations of Cantorvals to properties of countable linear orders and to show, applying the Mazurkiewicz--Sierpi\'nski Theorem (1920), that there exist continuum many non-homeomorphic L-Cantorvals.
Keywords
Cite
@article{arxiv.2312.13047,
title = {On compact subsets of the reals},
author = {Wojciech Bielas and Mateusz Kula and Szymon Plewik},
journal= {arXiv preprint arXiv:2312.13047},
year = {2023}
}