On compact subsets of the reals

2023/12/20 by Bielas, Wojciech, Kula, Mateusz, Plewik, Szymon · 1 citation
#26A03 #54F05 #54F65 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2312.13047

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--Sierpiński Theorem (1920), that there exist continuum many non-homeomorphic L-Cantorvals.

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