Spaces which Invert Weak Homotopy Equivalences

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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
Autor principal: Barmak, J.A.
Formato: INPR
Materias:
homotopy types
non-Hausdorff spaces
weak homotopy equivalences
Acceso en línea: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 todo:paper_00130915_v_n_p_Barmak
record_format dspace
spelling todo:paper_00130915_v_n_p_Barmak2023-10-03T14:10:41Z Spaces which Invert Weak Homotopy Equivalences Barmak, J.A. 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. INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Barmak, J.A.
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.
format INPR
author Barmak, J.A.
author_facet Barmak, J.A.
author_sort Barmak, J.A.
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
url http://hdl.handle.net/20.500.12110/paper_00130915_v_n_p_Barmak
work_keys_str_mv AT barmakja spaceswhichinvertweakhomotopyequivalences
_version_ 1807321272003067904

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