Results 291 to 300 of about 367,563 (325)
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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.
Nyikos, Peter, Zdomskyy, Lyubomyr
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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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About Weakly Locally Compact Spaces
2004In an L-topological space we present good definitions for weak local compactness. We obtain the regularity and a one point compactification theorem for weakly locally compact spaces.
Kudri, SRT +2 more
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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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More on countably compact, locally countable spaces
Israel Journal of Mathematics, 1988Following the paper of the author, \textit{Zs. Nagy} and \textit{W. Weiss} [Period. Math. Hung. 10, 193-206 (1979; Zbl 0418.54019)], a \(T_ 3\) space X is called good (splendid) if it is countably compact, locally countable (and \(\omega\)-fair). \(G(\kappa)\) (resp. \(S(\kappa)\)) denotes the statement that a good (resp. splendid) space X with \(| X| =
Juhász, István +2 more
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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Cosmology with the Laser Interferometer Space Antenna
Living Reviews in Relativity, 2023Germano Nardini
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Ab Initio Machine Learning in Chemical Compound Space
Chemical Reviews, 2021Bing Huang, O Anatole Von Lilienfeld
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