2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59201We show that the Bruschlinsky group with the winding order is a homeomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit space is a dimension group and is a quotient of the dimension group with the standard order of the adjacency matrices associated with the presentation.17 pages 4 figuresGeometric TopologyDynamical Systems54F15, 54F65, 06F20text