Essential families can be used to provide a simple characterization of the dimension of a normal space (and with a small adjustment, also for a regular space). For example, a normal space $X$ has dimension $n\in \mathbb{N}$ if and only if it has an essential family of cardinality $n$ and for all $m>n$, it has no essential family of cardinality $m$. A space is {\it strongly infinite-dimensional} if it has a countably infinite essential family. The Hilbert cube, $I^{\mathrm{\infty }}$, is strongly infinite-dimensional; however, one might wonder if it has an uncountable essential family. Going even further, can a separable metrizable space have an uncountable essential family?

In this talk we will define essential families as they are used in this setting and then present the following theorem which establishes an upper bound on the cardinality of essential families in normal or regular (${\mathrm{T}}_1$ not required) spaces.

{\bf Theorem.} Let $X$ be a regular or normal space of infinite weight and $\mathcal{C}$ be an essential family in $X$. Then $\mathrm{card}\mathcal{C}\le \mathrm{wt}X$.

We employ a proof by contradiction in which we assume that there is an essential family of higher cardinality than the weight of the given space and then by a transfinite construction, which we will not try to present, arrive at a contradiction. But we will give a clue as to how one can ``finesse’’ this supposedly essential family in order to detect that it is not essential.