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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Lenguaje: | eng |
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2005
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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 |
record_format | invenio |
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 |