This research demonstrates that essential families in regular or normal spaces are limited by the space's weight, indicating implications for separable spaces.
Let \(X\) be a regular or normal space (\(T_1\) not required) with infinite weight and \(C\) be an essential family in \(X\). We will show that \({card}\, C≤{wt}\, X\). This implies that every essential family in a separable metrizable space is countable.
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Leonard R. Rubin (2026) studied this question.
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