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arXiv · 2602.15542

Homeomorphisms between compact subsets of real numbers

Sławomir Kusiński·Szymon Plewik
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Abstract

We first present a reduction of properties of compact sets of real numbers to properties of countable orders. Then discuss a variant of homogeneity of compact subsets of real numbers, focusing on the family of $t$-sets. Finally, we prove that there are exactly $\omega_1$ many non-homeomorphic $t$-sets.

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Sławomir Kusiński, Szymon Plewik. 2026-02-17. Homeomorphisms between compact subsets of real numbers. https://arxiv.org/abs/2602.15542

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