Topological Transcendental Fields
| Autor: | Chalebgwa, Taboka Prince, Morris, Sidney A. |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | This article initiates the study of topological transcendental fields $\FF$ which are subfields of the topological field $\CC$ of all complex numbers such that $\FF$ consists of only rational numbers and a nonempty set of transcendental numbers. $\FF$, with the topology it inherits as a subspace of $\CC$, is a topological field. Each topological transcendental field is a separable metrizable zero-dimensional space and algebraically is $\QQ(T)$, the extension of the field of rational numbers by a set $T$ of transcendental numbers. It is proved that there exist precisely $2^{\aleph_0}$ countably infinite topological transcendental fields and each is homeomorphic to the space $\QQ$ of rational numbers with its usual topology. It is also shown that there is a class of $2^{2^{\aleph_0} }$ of topological transcendental fields of the form $\QQ(T)$ with $T$ a set of Liouville numbers, no two of which are homeomorphic. Comment: 6 pages |
| Databáze: | arXiv |
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