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Some duality properties of non-saddle sets Giraldo, A. Alonso Morón, Manuel Romero Ruiz Del Portal, Francisco Rodríguez Sanjurjo, José Manuel We show in this paper that the class of compacts that call be isolated non-saddle sets of flows in ANRs is precisely the class of compacta with polyhedral shape. We also prove-reinforcing the essential role played by shape theory in this setting-that the Conley index of a regular isolated non-saddle set is determined, in certain cases, by its shape. We finally introduce and study the notion of dual of a non-saddle set. Examples of compacta related by duality are attractor-repeller pairs. We use the complement theorems in shape theory to prove that the shape of the dual set is determined by the shape of the original non-saddle set. 2023-06-20T16:52:29Z 2023-06-20T16:52:29Z 2001-06-29 journal article Giraldo, A., Alonso Morón, M., Romero Ruiz Del Portal, F., Rodríguez Sanjurjo, J. M. «Some Duality Properties of Non-Saddle sets☆☆The Authors Are Supported by DGESIC.» Topology and Its Applications, vol. 113, n.o 1-3, junio de 2001, pp. 51-59. DOI.org (Crossref), https://doi.org/10.1016/S0166-8641(00)00017-1. 0166-8641 10.1016/S0166-8641(00)00017-1 https://hdl.handle.net/20.500.14352/57293 https//doi.org/10.1016/S0166-8641(00)00017-1 http://www.sciencedirect.com/science/article/pii/S0166864100000171 eng open access Elsevier Science