On Gruenhage spaces, separating σ-isolated families, and their relatives
| Contribuinte(s) |
Universidad de Alicante. Departamento de Matemática Aplicada Sistémica, Cibernética y Optimización (SCO) |
|---|---|
| Data(s) |
22/09/2016
22/09/2016
01/09/2015
|
| Resumo |
We prove that, given a topological space X, the following conditions are equivalent. (α) X is a Gruenhage space. (β) X has a countable cover by sets of small local diameter (property SLD) by F∩G sets. (γ) X has a separating σ-isolated family M⊂F∩G. (δ) X has a one-to-one continuous map into a metric space which has a σ-isolated base of F∩G sets. Besides, we provide an example which shows Fragmentability ⇏ property SLD ⇏ the space to be Gruenhage. This work has been partially supported by the Generalitat Valenciana project GV/2014/072 and Universidad de Alicante project GRE11-08. |
| Identificador |
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 2015, 109(2): 717-730. doi:10.1007/s13398-014-0211-5 1578-7303 (Print) 1579-1505 (Online) http://hdl.handle.net/10045/58142 10.1007/s13398-014-0211-5 |
| Idioma(s) |
eng |
| Publicador |
Springer Milan |
| Relação |
http://dx.doi.org/10.1007/s13398-014-0211-5 |
| Direitos |
© Springer-Verlag Italia 2014. The final publication is available at Springer via http://dx.doi.org/10.1007/s13398-014-0211-5 info:eu-repo/semantics/openAccess |
| Palavras-Chave | #Gruenhage space #σ-Isolated family #Countable cover by sets of small local diameter #Fragmentability #Descriptive compact #Matemática Aplicada |
| Tipo |
info:eu-repo/semantics/article |
