| Autor: |
Taboka Prince Chalebgwa, Sidney A. Morris |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Axioms, Vol 11, Iss 3, p 118 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2075-1680 |
| DOI: |
10.3390/axioms11030118 |
| Popis: |
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 2ℵ0 countably infinite topological transcendental fields and each is homeomorphic to the space Q of rational numbers with its usual topology. It is also shown that there is a class of 22ℵ0 of topological transcendental fields of the form Q(T) with T a set of Liouville numbers, no two of which are homeomorphic. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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