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Small Valdivia compact spaces

We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\loe\aleph_1$ is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps...

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Detalles Bibliográficos
Autores principales: Kubi's, W, Michalewski, H
Lenguaje:eng
Publicado: 2005
Materias:
Acceso en línea:http://cds.cern.ch/record/850176
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author Kubi's, W
Michalewski, H
author_facet Kubi's, W
Michalewski, H
author_sort Kubi's, W
collection CERN
description We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\loe\aleph_1$ is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight at most $\aleph_1$ is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors.
id cern-850176
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2005
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spelling cern-8501762019-09-30T06:29:59Zhttp://cds.cern.ch/record/850176engKubi's, WMichalewski, HSmall Valdivia compact spacesMathematical Physics and MathematicsWe prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\loe\aleph_1$ is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight at most $\aleph_1$ is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors.math.GN/0507062oai:cds.cern.ch:8501762005-07-04
spellingShingle Mathematical Physics and Mathematics
Kubi's, W
Michalewski, H
Small Valdivia compact spaces
title Small Valdivia compact spaces
title_full Small Valdivia compact spaces
title_fullStr Small Valdivia compact spaces
title_full_unstemmed Small Valdivia compact spaces
title_short Small Valdivia compact spaces
title_sort small valdivia compact spaces
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/850176
work_keys_str_mv AT kubisw smallvaldiviacompactspaces
AT michalewskih smallvaldiviacompactspaces