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arXiv · 1811.04325

On (ultra-) completeness numbers and (pseudo-) paving numbers

Frédéric Mynard
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Abstract

We study the completeness and ultracompleteness numbers of a convergence space. In the case of a completely regular topological space, the completeness number is countable if and only if the space is $\v{C}$ech-complete, and the ultracompleteness number is countable if and only if the space is ultracomplete. We show that the completeness number of a space is equal to the pseudopaving number of the upper Kuratowski convergence on the space of its closed subsets, at $\emptyset$. Similarly, the ultracocompleteness number of a space is equal to the paving number of the upper Kuratowski convergence on the space of its closed subsets, at $\emptyset$.

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Frédéric Mynard. 2018-11-10. On (ultra-) completeness numbers and (pseudo-) paving numbers. https://doi.org/10.1016/j.topol.2019.01.006

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