2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64060We introduce the notion of weakly (strongly) infinite real rank for unital $C^{\ast}$-algebras. It is shown that a compact space $X$ is weakly (strongly) infine-dimensional if and only if $C(X)$ has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group $C^{\ast}$-algebra $C^{\ast}({\mathbb F}_{\infty})$ of the free group on countable number of generators has strongly infinite real rank.9 pagesGeneral TopologyFunctional Analysis54F45, 46L05text