Homotopic properties of confluent maps in the proper category |
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Authors: | T. Ferná ndez-Bayort,A. Quintero |
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Affiliation: | a C.G.A. (Centro de Gestión Avanzado), Consejería de Educación, Junta de Andalucía, Edificio Torretriana, planta 1, 41071 Sevilla, Spain b Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Apartado 1160, 41080 Sevilla, Spain |
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Abstract: | We establish some properties of homotopical nature for confluent maps in the proper category. We analyze in this setting the characterization of tree-like continua by J.H. Case and R.E. Chamberlin as well as the theorem by T.B. McLean on the preservation of tree-likeness under confluent maps. We give counterexamples for the corresponding proper analogues and we extend results of several authors in classical continuum theory to non-compact spaces. Finally, we describe the behavior of these maps with respect to the fundamental pro-group, generalizing results of J. Grispolakis and other authors. Two questions of interest are still open (Open Question 15 and Conjecture 24). |
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Keywords: | 54C10 54F15 54D35 |
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