- Title
- Topological transcendental fields
- Creator
- Chalebgwa, Taboka; Morris, Sidney
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/188613
- Identifier
- vital:17295
- Identifier
-
https://doi.org/10.3390/axioms11030118
- Identifier
- ISSN:2075-1680 (ISSN)
- Abstract
- This article initiates the study of topological transcendental fields F which are subfields of the topological field C of all complex numbers such that F only consists of rational numbers and a nonempty set of transcendental numbers. F, with the topology it inherits as a subspace of C, is a topological field. Each topological transcendental field is a separable metrizable zero-dimensional space and algebraically is Q(T), the extension of the field of rational numbers by a set T of transcendental numbers. It is proven that there exist precisely 222ℵ0 of topological transcendental fields of the form ℚ(𝑇) with T a set of Liouville numbers, no two of which are homeomorphic.
- Publisher
- MDPI
- Relation
- Axioms Vol. 11, no. 3 (2022), p.
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- https://creativecommons.org/licenses/by/4.0/
- Rights
- Copyright © 2022 by the authors
- Rights
- Open Access
- Subject
- 49 Mathematical Sciences; Algebraic; Countably infinite; Extension field; Homeomorphic; Subfield; Topological field; Transcendental number
- Full Text
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