Wojciech Bielas, Mateusz Kula, Szymon Plewik
Published 2023-12-20Version 1
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.
Haar meager sets, their hulls, and relationship to compact sets
On Mazurkiewicz's sets, thin σ-ideals of compact sets and the space of probability measures on the rationals
Topological gyrogroups with Frechet-Urysohn property and omega^{omega}-base
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