2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77094Various notions of stable ranks are studied for topological algebras. Some partial answers to R.G. Swan's problem (Have two Banach or good Fréchet algebras as in the density theorem in K-theory the same stable rank ?) are obtained. For example, a Fréchet dense $\ast$-subalgebra $A$ of a $C^\ast$-algebra $B$, closed under $C^\infty$-functional calculus of self-adjoint elements, has the same Bass stable rank as $B$.AMS-LaTeX, 29 pages, submitted to J. Funct. AnalOperator AlgebrasFunctional Analysistext