2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60382We show that the family of nest algebras with $r$ non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local characterisation of limits formed from this family. We then consider quite general regular limit algebras and characterise these algebras using a local condition which reflects the assumed regularity of the system.20 pagesOperator Algebras47L40, 47A55text