2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65244We construct compact quantum metric spaces (CQMS) starting with some C*algebra extension with a positive splitting. As special cases we discuss the case of Toeplitz algebra, quantum SU(2) and Podles sphere.Operator AlgebrasFunctional Analysis46L87(primary),58B34(secondary)From C*algebra extensions to CQMS, ${SU}_q(2)$, Podles sphere and other examplestext