One point reductions of finite spaces, h-regular CW-complexes and collapsibility
We investigate one point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of h-regular C W -complex, generalizing the concept of regular CW -complex, an...
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2008
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14722747_v8_n3_p1763_Barmak http://hdl.handle.net/20.500.12110/paper_14722747_v8_n3_p1763_Barmak |
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| Sumario: | We investigate one point reduction methods of finite topological spaces. These methods allow one to study homotopy theory of cell complexes by means of elementary moves of their finite models. We also introduce the notion of h-regular C W -complex, generalizing the concept of regular CW -complex, and prove that the h-regular CW -complexes, which are a sort of combinatorial uptohomotopy objects, are modeled (up to homotopy) by their associated finite spaces. This is accomplished by generalizing a classical result of McCord on simplicial complexes. © 2008 Mathematical Sciences Publishers. |
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