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2020 A series of series topologies on $\mathbb{N}$
Jason DeVito, Zachary Parker
Involve 13(2): 205-218 (2020). DOI: 10.2140/involve.2020.13.205

Abstract

Each series n=1an of real strictly positive terms gives rise to a topology on ={1,2,3,} by declaring a proper subset A to be closed if nAan<. We explore the relationship between analytic properties of the series and topological properties on . In particular, we show that, up to homeomorphism, ||-many topologies are generated. We also find an uncountable family of examples {α}α[0,1] with the property that for any α<β, there is a continuous bijection βα, but the only continuous functions αβ are constant.

Citation

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Jason DeVito. Zachary Parker. "A series of series topologies on $\mathbb{N}$." Involve 13 (2) 205 - 218, 2020. https://doi.org/10.2140/involve.2020.13.205

Information

Received: 27 February 2019; Revised: 7 July 2019; Accepted: 3 December 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07184481
MathSciNet: MR4080491
Digital Object Identifier: 10.2140/involve.2020.13.205

Subjects:
Primary: 54A10, 54G99

Rights: Copyright © 2020 Mathematical Sciences Publishers

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