Spaces which Invert Weak Homotopy Equivalences
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] ?†...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
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Cambridge University Press
2018
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
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| 005 | 20230518205717.0 | ||
| 008 | 190410s2018 xx ||||fo|||| 00| 0 eng|d | ||
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| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Barmak, J.A. | |
| 245 | 1 | 0 | |a Spaces which Invert Weak Homotopy Equivalences |
| 260 | |b Cambridge University Press |c 2018 | ||
| 270 | 1 | 0 | |m Barmak, J.A.; Departamento de Matemática, Universidad de Buenos Aires, Facultad de Ciencias Exactas y NaturalesArgentina; email: jbarmak@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 520 | 3 | |a 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. |l eng | |
| 536 | |a Article in Press | ||
| 593 | |a Departamento de Matemática, Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Buenos Aires, Argentina | ||
| 593 | |a CONICET-Universidad de Buenos Aires, Instituto de Investigaciones Matemáticas Luis A. Santaló (IMAS), Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a HOMOTOPY TYPES |
| 690 | 1 | 0 | |a NON-HAUSDORFF SPACES |
| 690 | 1 | 0 | |a WEAK HOMOTOPY EQUIVALENCES |
| 773 | 0 | |d Cambridge University Press, 2018 |p Proc. Edinburgh Math. Soc. |x 00130915 |t Proceedings of the Edinburgh Mathematical Society | |
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| 856 | 4 | 0 | |u https://doi.org/10.1017/S0013091518000639 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00130915_v_n_p_Barmak |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00130915_v_n_p_Barmak |y Registro en la Biblioteca Digital |
| 961 | |a paper_00130915_v_n_p_Barmak |b paper |c PE | ||
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| 999 | |c 86214 | ||