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arXiv · 2307.07223

Closed copies of $\mathbb{N}$ in $\mathbb{R}^{\omega_1}$

Alan Dow·Klaas Pieter Hart·Jan van Mill·Hans Vermeer
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Abstract

We investigate closed copies of~$\mathbb{N}$ in powers of~$\mathbb{R}$ with respect to $C^*$- and $C$-embedding. We show that $\mathbb{R}^{\omega_1}$ contains closed copies of~$\mathbb{N}$ that are not $C^*$-embedded.

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Alan Dow, Klaas Pieter Hart, Jan van Mill, Hans Vermeer. 2023-07-14. Closed copies of $\mathbb{N}$ in $\mathbb{R}^{\omega_1}$. https://doi.org/10.1016/j.topol.2025.109514

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