Izvorni znanstveni članak

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

Sažetak

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.

Ključne riječi

Cardinality; essential family; normal space; regular space; weight

Hrčak ID:

344369

URI

https://hrcak.srce.hr/344369

Datum izdavanja:

10.2.2026.

Posjeta: 219 *