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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Detalles Bibliográficos
Publicado: 2018
Materias:
homotopy types
non-Hausdorff spaces
weak homotopy equivalences
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00130915_v_n_p_Barmak
http://hdl.handle.net/20.500.12110/paper_00130915_v_n_p_Barmak
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00130915_v_n_p_Barmak
record_format dspace
spelling paper:paper_00130915_v_n_p_Barmak2023-06-08T14:35:39Z Spaces which Invert Weak Homotopy Equivalences homotopy types non-Hausdorff spaces 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] ?†' [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. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00130915_v_n_p_Barmak http://hdl.handle.net/20.500.12110/paper_00130915_v_n_p_Barmak
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic homotopy types
non-Hausdorff spaces
weak homotopy equivalences
spellingShingle homotopy types
non-Hausdorff spaces
weak homotopy equivalences
Spaces which Invert Weak Homotopy Equivalences
topic_facet homotopy types
non-Hausdorff spaces
weak homotopy equivalences
description 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.
title Spaces which Invert Weak Homotopy Equivalences
title_short Spaces which Invert Weak Homotopy Equivalences
title_full Spaces which Invert Weak Homotopy Equivalences
title_fullStr Spaces which Invert Weak Homotopy Equivalences
title_full_unstemmed Spaces which Invert Weak Homotopy Equivalences
title_sort spaces which invert weak homotopy equivalences
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00130915_v_n_p_Barmak
http://hdl.handle.net/20.500.12110/paper_00130915_v_n_p_Barmak
_version_ 1768544578583920640

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