Original scientific paper
https://doi.org/10.21857/yl4okfkgv9
The maximum cardinality of essential families in regular or normal spaces
Leonard R. Rubin
; Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA
Abstract
Let \(X\) be a regular or normal space (\(\mathrm{T}_1\) not required) with infinite weight
and \(\mathcal{C}\) be an essential family in \(X\).
We will show that \({\operatorname{card}}\, \mathcal{C}\leq{\operatorname{wt}}\, X\). This implies that every essential family
in a separable metrizable space is countable.
Keywords
Cardinality; essential family; normal space; regular space; weight
Hrčak ID:
344369
URI
Publication date:
10.2.2026.
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