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00925njm 22002777a 4500 dc Martínez Pérez, Álvaro author Alonso Morón, Manuel author 2010-10-01 In this paper we prove that if we consider the standard real metric on simplicial rooted trees then the category Tower-Set of inverse sequences can be described by means of the bounded coarse geometry of the naturally associated trees. Using this we give a geometrical characterization of Mittag-Leffler property in inverse sequences in terms of the metrically proper homotopy type of the corresponding tree and its maximal geodesically complete subtree. We also obtain some consequences in shape theory. In particular we describe some new representations of shape morphisms related to infinite branches in trees. Martínez Pérez, Á. y Alonso Morón, M. «Inverse Sequences, Rooted Trees and Their End Spaces». Topology and Its Applications, vol. 157, n.o 16, octubre de 2010, pp. 2480-94. DOI.org (Crossref), https://doi.org/10.1016/j.topol.2010.08.005. 0166-8641 10.1016/j.topol.2010.08.005 https://hdl.handle.net/20.500.14352/42137 https//doi.org/10.1016/j.topol.2010.08.005 http://www.sciencedirect.com/science/article/pii/S0166864110002634 Inverse sequences, rooted trees and their end spaces