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Error Resilient Space Partitioning. [PDF]
Discrete Comput GeomDunkelman O +6 more
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Applied Categorical Structures, 2005
The author shows that the space \(X^{[0,1]}\) of continuous maps \([0,1]\to X\) with the compact-open topology is not locally compact for any space \(X\) having a nonconstant path of closed points. For a \(T_1\)-space, it follows that \(X^{[0,1]}\) is locally compact if and only if \(X\) is locally compact and totally path disconnected, where \(X\) is ...
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The author shows that the space \(X^{[0,1]}\) of continuous maps \([0,1]\to X\) with the compact-open topology is not locally compact for any space \(X\) having a nonconstant path of closed points. For a \(T_1\)-space, it follows that \(X^{[0,1]}\) is locally compact if and only if \(X\) is locally compact and totally path disconnected, where \(X\) is ...
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Locally compact, ω1-compact spaces
Annals of Pure and Applied LogicAn $ω_1$-compact space is a space in which every closed discrete subspace is countable. We give various general conditions under which a locally compact, $ω_1$-compact space is $σ$-countably compact, i.e., the union of countably many countably compact spaces. These conditions involve very elementary properties.
Peter Nyikos, Lyubomyr Zdomskyy
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On computably locally compact Hausdorff spaces
Mathematical Structures in Computer Science, 2009Locally compact Hausdorff spaces generalise Euclidean spaces and metric spaces from ‘metric’ to ‘topology’. But does the effectivity on the latter (Brattka and Weihrauch 1999; Weihrauch 2000) still hold for the former? In fact, some results will be totally changed.
Yatao Xu, Tanja Grubba
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On the local compactness of spaces of positive measures
Statistics & Probability Letters, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1995
A topological space is locally compact if every point has an open nbhd with compact closure. Clearly, compact spaces and closed subspaces of locally compact spaces are locally compact. Products of finitely many locally compact spaces are locally compact iff all but finitely many of the factors are compact.
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A topological space is locally compact if every point has an open nbhd with compact closure. Clearly, compact spaces and closed subspaces of locally compact spaces are locally compact. Products of finitely many locally compact spaces are locally compact iff all but finitely many of the factors are compact.
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1950
In this section we shall derive a few auxiliary topological results which, because of their special nature, are usually not discussed in topology books.
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In this section we shall derive a few auxiliary topological results which, because of their special nature, are usually not discussed in topology books.
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On locally compact paracompact spaces
1978Viene data una dimostrazione elementare del fatto che il prodotto cartesiano di un'infinità numerabile di spazi localmente compatti e paracom¬patti è uno spazio paracompatto. Infine si caratterizzano gli spazi ereditariamente paracompatti e perfettamente normali.
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