We present internal characterizations for an inverse system of compact Hausdorff spaces that show when its limit will be strongly infinite-dimensional, weakly infinite-dimensional, or have its dimension $n\in {\mathbb{N}}_{\ge 0}$. Our main tool involves lifting the notion of an essential family into a parallel concept for inverse systems. In our presentation we plan to review the definitions of essential family, strong and weak infinite-dimensionality, finite dimensionality, and inverse systems. After doing that, we will state our main results but will not go into any proofs. The published paper with all details appears in Rad Hazu. Matematičke Znanosti, v. 29=564 (2025): 299-318.

This is joint work with Matthew Lynam, East Central University