Jardón Arcos, D.; Tkachuk, VV. (2006). When is an ultracomplete space almost locally compact?. Applied General Topology. 7(2):191-201. https://doi.org/10.4995/agt.2006.1923
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/83018
Title:
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When is an ultracomplete space almost locally compact?
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Author:
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Jardón Arcos, Daniel
Tkachuk, Vladimir V.
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Issued date:
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Abstract:
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[EN] We study spaces X which have a countable outer base in βX; they are called ultracomplete in the most recent terminology. Ultracompleteness implies Cech-completeness and is implied by almost local compactness (≡having ...[+]
[EN] We study spaces X which have a countable outer base in βX; they are called ultracomplete in the most recent terminology. Ultracompleteness implies Cech-completeness and is implied by almost local compactness (≡having all points of non-local compactness inside a compact subset of countable outer character). It turns out that ultracompleteness coincides with almost local compactness in most important classes of isocompact spaces (i.e., in spaces in which every countably compact subspace is compact). We prove that if an isocompact space X is ω-monolithic then any ultracomplete subspace of X is almost locally compact. In particular, any ultracomplete subspace of a compact ω-monolithic space of countable tightness is almost locally compact. Another consequence of this result is that, for any space X such that vX is a Lindelöf Σ-space, a subspace of Cp(X) is ultracomplete if and only if it is almost locally compact. We show that it is consistent with ZFC that not all ultracomplete subspaces of hereditarily separable compact spaces are almost locally compact.
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Subjects:
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Ultracompleteness
,
Cech-completeness
,
Countable type
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Pointwise countable type
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Lindelöf Σ-spaces
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Splittable spaces
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Eberlein compact spaces
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Almost locally compact spaces
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Isocompact spaces
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Copyrigths:
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Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
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Source:
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Applied General Topology. (issn:
1576-9402
) (eissn:
1989-4147
)
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DOI:
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10.4995/agt.2006.1923
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Publisher:
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Universitat Politècnica de València
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Publisher version:
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https://doi.org/10.4995/agt.2006.1923
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Project ID:
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info:eu-repo/grantAgreement/CONACyT//94897/
info:eu-repo/grantAgreement/CONACyT//400200-5-38164-E/
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Thanks:
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Research supported by Consejo Nacional de Ciencia y Tecnología (CONACyT) of Mexico grants 94897 and 400200-5-38164-E.
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Type:
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Artículo
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