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2018 Some Applications of Order-Embeddings of Countable Ordinals into the Real Line
Leonard Huang
Real Anal. Exchange 43(2): 417-428 (2018). DOI: 10.14321/realanalexch.43.2.0417

Abstract

It is a well-known fact that an ordinal \( \alpha \) can be embedded into the real line \( \mathbb{R} \) in an order-preserving manner if and only if \( \alpha \) is countable. However, it would seem that outside of set theory, this fact has not yet found any concrete applications. The goal of this paper is to present some applications. More precisely, we show how two classical results, one in point-set topology and the other in real analysis, can be proven by defining specific order-embeddings of countable ordinals into \( \mathbb{R} \).

Citation

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Leonard Huang. "Some Applications of Order-Embeddings of Countable Ordinals into the Real Line." Real Anal. Exchange 43 (2) 417 - 428, 2018. https://doi.org/10.14321/realanalexch.43.2.0417

Information

Published: 2018
First available in Project Euclid: 27 June 2018

zbMATH: 06924898
MathSciNet: MR3942587
Digital Object Identifier: 10.14321/realanalexch.43.2.0417

Subjects:
Primary: 03E10, 54A05
Secondary: 26A24

Rights: Copyright © 2018 Michigan State University Press

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Vol.43 • No. 2 • 2018
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