On monotonous separately continuous functions
[EN] Let T = (T, ≤) and T1= (T1 , ≤1) be linearly ordered sets and X be a topological space. The main result of the paper is the following: If function ƒ(t,x) : T × X → T1 is continuous in each variable (“t” and “x”) separately and function ƒx(t) = ƒ(t,x) is monotonous on T for every x ∈ X, then ƒ i...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/118960 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/118960 |
| Access Level: | acceso abierto |
| Palabra clave: | Separately continuous mappings Linearly ordered topological spaces Young&apos s theorem |
| Sumario: | [EN] Let T = (T, ≤) and T1= (T1 , ≤1) be linearly ordered sets and X be a topological space. The main result of the paper is the following: If function ƒ(t,x) : T × X → T1 is continuous in each variable (“t” and “x”) separately and function ƒx(t) = ƒ(t,x) is monotonous on T for every x ∈ X, then ƒ is continuous mapping from T × X to T1, where T and T1 are considered as topological spaces under the order topology and T × X is considered as topological space under the Tychonoff topology on the Cartesian product of topological spaces T and X. |
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