Real Analysis Exchange

Some Applications of Order-Embeddings of Countable Ordinals into the Real Line

Leonard Huang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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 \( \mathbb{R} \).

Article information

Source
Real Anal. Exchange, Volume 43, Number 2 (2018), 417-428.

Dates
First available in Project Euclid: 27 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.rae/1530064970

Digital Object Identifier
doi:10.14321/realanalexch.43.2.0417

Mathematical Reviews number (MathSciNet)
MR3942587

Zentralblatt MATH identifier
06924898

Subjects
Primary: 03E10: Ordinal and cardinal numbers 54A05: Topological spaces and generalizations (closure spaces, etc.)
Secondary: 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]

Keywords
cardinal ordinal order-embedding symmetric derivative Quasi-Mean Value Theorem

Citation

Huang, Leonard. Some Applications of Order-Embeddings of Countable Ordinals into the Real Line. Real Anal. Exchange 43 (2018), no. 2, 417--428. doi:10.14321/realanalexch.43.2.0417. https://projecteuclid.org/euclid.rae/1530064970


Export citation