It is well known that if X is a CW-complex, then for every weak homotopy equivalence f: A ?†' B, the map f∗: [X, A] ?†' [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes have that property. Now, for which spaces X is f∗: [B, X] ?†' [A, X] a bijection for every weak equivalence f? This question was considered by J. Strom and T. Goodwillie. In this note we prove that a non-empty space inverts weak equivalences if and only if it is contractible. Copyright © Edinburgh Mathematical Society 2018.
| Documento: | Artículo |
| Título: | Spaces which Invert Weak Homotopy Equivalences |
| Autor: | Barmak, J.A. |
| Filiación: | Departamento de Matemática, Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Buenos Aires, Argentina CONICET-Universidad de Buenos Aires, Instituto de Investigaciones Matemáticas Luis A. Santaló (IMAS), Buenos Aires, Argentina |
| Palabras clave: | homotopy types; non-Hausdorff spaces; weak homotopy equivalences |
| Año: | 2018 |
| DOI: | http://dx.doi.org/10.1017/S0013091518000639 |
| Título revista: | Proceedings of the Edinburgh Mathematical Society |
| Título revista abreviado: | Proc. Edinburgh Math. Soc. |
| ISSN: | 00130915 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00130915_v_n_p_Barmak |
