Mathematics > General Topology
arXiv:2602.15542 (math)
[Submitted on 17 Feb 2026 (v1), last revised 2 Jun 2026 (this version, v2)]
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.
| Comments: | Acknowledgment: We would like to thank W. Bielas and T. Kania for their comments, which allowed us to remove typos and ambiguities from the version previously published at arXiv |
| Subjects: | General Topology (math.GN); Logic (math.LO) |
| MSC classes: | 26A03, 54F05 |
| Cite as: | arXiv:2602.15542 [math.GN] |
| (or arXiv:2602.15542v2 [math.GN] for this version) | |
| https://doi.org/10.48550/arXiv.2602.15542 arXiv-issued DOI via DataCite |
Submission history
From: Sławomir Kusiński [view email]
[v1]
Tue, 17 Feb 2026 12:48:32 UTC (16 KB)
[v2]
Tue, 2 Jun 2026 14:12:20 UTC (18 KB)
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