On uniformly continuous functions between pseudometric spaces and the Axiom of Countable Choice
| Autor: | Samuel G. da Silva |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Logic 010102 general mathematics Axiom of countable choice Mathematics::General Topology 0102 computer and information sciences Pseudometric space Characterization (mathematics) 01 natural sciences Philosophy Uniform continuity Metric space 010201 computation theory & mathematics 0101 mathematics Algebra over a field Mathematics |
| Zdroj: | Archive for Mathematical Logic. 58:353-358 |
| ISSN: | 1432-0665 0933-5846 |
| DOI: | 10.1007/s00153-018-0643-2 |
| Popis: | In this note we show that the Axiom of Countable Choice is equivalent to two statements from the theory of pseudometric spaces: the first of them is a well-known characterization of uniform continuity for functions between (pseudo)metric spaces, and the second declares that sequentially compact pseudometric spaces are $$\mathbf {UC}$$ —meaning that all real valued, continuous functions defined on these spaces are necessarily uniformly continuous. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink