I-Fréchet-Urysohn property in Cα(X)
[EN] In this paper, we introduce I-Fr´echet-Urysohn, strongly I-Fr´echet-Urysohn and strictly I-Fr´echet-Urysohn spaces,discuses their properties of countable tightness and mappings that preserve these spaces.Meanwhile, we discuss the internal characterizations of these spaces in C?(X).The following...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:riunet______::a7f27194bbbc30672d5f9041cbe232dc |
| Acceso en línea: | https://riunet.upv.es/handle/10251/233563 |
| Access Level: | acceso abierto |
| Palabra clave: | I-Fréchet-Urysohn spaces strongly I-Fréchet-Urysohn spaces strictly IFréchet-Urysohn spaces Countable tightness Set-open topology Functional spaces |
| Sumario: | [EN] In this paper, we introduce I-Fr´echet-Urysohn, strongly I-Fr´echet-Urysohn and strictly I-Fr´echet-Urysohn spaces,discuses their properties of countable tightness and mappings that preserve these spaces.Meanwhile, we discuss the internal characterizations of these spaces in C?(X).The following main theorem is obtained. Theorem. Let ? be a network of X. The following are equivalent. (1) Cα(X) is a strictly I-Fr´echet-Urysohn space. (2) Cα(X) is a strongly I-Fr´echet-Urysohn space. (3) Cα(X) is an I-Fr´echet-Urysohn space. (4) Every open α-cover of X contains an I-α-sequence. (5) If {Un}n∈N is a sequence of open α-cover of X, then there is an I-α-sequence {un}n∈N of X such that each un ∈ Un. (6) Cωα (X) is a strictly I-Fréchet-Urysohn space. |
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