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uid: P000145
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name: Strongly paracompact
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aliases:
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- Hypocompact
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refs:
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- zb: "0684.54001"
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name: General Topology (Engelking, 1989)
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- zb: "0207.52704"
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name: On some generalized compactness properties (J. Greever)
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Every open cover has a star-finite open refinement.
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A family $\mathscr A$ of subsets of $X$ is called *star-finite* if each element of $\mathscr A$ meets at most finitely many elements of $\mathscr A$.
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Defined on p. 326 of {{zb:0684.54001}} together with the condition that the space is {P3}. Here we do not assume any separation axiom as part of the definition.
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Also called *hypocompact*, for example in Definition 2 of {{zb:0207.52704}}.
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