Ayala Gómez, RafaelFernández Fernández, Luis ManuelVilches Alarcón, José Antonio2016-09-162016-09-162008Ayala Gómez, R., Fernández Fernández, L.M. y Vilches Alarcón, J.A. (2008). Critical elements of proper discrete Morse functions. Mathematica Pannonica, 19 (2), 171-185.0865-2090http://hdl.handle.net/11441/45081The aim of this paper is to study the notion of critical element of a proper discrete Morse function defined on non-compact graphs and surfaces. It is an extension to the non-compact case of the concept of critical simplex which takes into account the monotonous behaviour of a function at the ends of a complex. We show how the number of critical elements are related to the topology of the complex.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Discrete Morse functionDiscrete Morse inequalitiesLocally finite complexCritical simplexDecreasing rayinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess