Spaces splittable over the class of Eberlein and descriptive compact spaces
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https://doi.org/10.1007/s13398-016-0364-5 |
Metadatos
Título
Spaces splittable over the class of Eberlein and descriptive compact spacesFecha de publicación
2018Editor
Springer MilanISSN
1578-7303; 1579-1505Cita bibliográfica
JARDÓN, Daniel; SANCHIS, Manuel. Spaces splittable over the class of Eberlein and descriptive compact spaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018, vol. 112, núm. 1, p. 57-70Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://link.springer.com/article/10.1007/s13398-016-0364-5Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
We study splittability over some classes of compact spaces which are useful in functional analysis and general topology. Among other things we show that a scattered pseudocompact space splittable over the class of ... [+]
We study splittability over some classes of compact spaces which are useful in functional analysis and general topology. Among other things we show that a scattered pseudocompact space splittable over the class of Eberlein compact spaces is Eberlein compact. We also prove that a compact space splittable over the class of Eberlein compact spaces is hereditarily σ-metacompact, and that if X is a compact space splittable over the class of Corson compact spaces, then d(X)=w(X). We also obtain several results on Rosenthal and on descriptive compact spaces. For instance: (1) a compact space is Rosenthal if and only if it is splittable over the class of Rosenthal compacta, (2) c-metrizable countably compact spaces which split over the class of descriptive compacta are descriptive compact spaces, (3) if X is a compact space splittable over the class of descriptive compact spaces, then hd(X)=w(X), (4) scattered compact spaces splittable over the class of descriptive compact spaces are σ-discrete descriptive compacta, and (5) it is consistent with ZFC that a compact space which splits over the class of descriptive compacta is a descriptive compact space. [-]
Publicado en
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018, vol. 112, núm. 1, p. 57-70Proyecto de investigación
D. Jardón was supported by Conacyt Grant 261983 and M. Sanchis was supported by Universitat Jaume I Grant P1⋅1B2014–35 and Generalitat Valenciana Grant AICO/2016/030.Derechos de acceso
© Springer-Verlag Italia 2016
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