“Mesocompact space”的意思、由来-开放百科全书

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Mesocompact space

释义

Notes
References

In mathematics, in the field of general topology, a topological space is said to be mesocompact if every open cover has a compact-finite open refinement.^[1] That is, given any open cover, we can find an open refinement with the property that every compact set meets only finitely many members of the refinement.^[2]

The following facts are true about mesocompactness:

Every compact space, and more generally every paracompact space is mesocompact. This follows from the fact that any locally finite cover is automatically compact-finite.
Every mesocompact space is metacompact, and hence also orthocompact. This follows from the fact that points are compact, and hence any compact-finite cover is automatically point finite.

Notes

1. ^Hart, Nagata & Vaughan, p200
2. ^Pearl, p23

References

{{Citation|editor1=K.P. Hart|editor2=J. Nagata|editor3=J.E. Vaughan|title=Encyclopedia of General Topology|publisher=Elsevier|year=2004|isbn=0-444-50355-2}}
{{Citation|editor-first=Elliott|editor-last=Pearl|title=Open Problems in Topology II|year=2007|isbn=0-444-52208-5|publisher=Elsevier}}

2 : Compactness (mathematics)|Properties of topological spaces

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