Adjointness of Suspension and Shape Path Functors
In this paper, we introduce a subcategory ∼Sh* of Sh* and obtain some results in this subcategory. First we show that there is a natural bijection Sh(∑(X, x), (Y,y))≅Sh((X,x),Sh((I, Ī),(Y,y))), for every (Y,y)∈ ~Sh* and (X,x)∈ Sh*. By this fact, we prove that for any pointed topological space (X,x)...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Kashan
2021-03-01
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| Series: | Mathematics Interdisciplinary Research |
| Subjects: | |
| Online Access: | https://mir.kashanu.ac.ir/article_111348_a639434f373b5e2c1e63558d731d8772.pdf |
| _version_ | 1797630850116878336 |
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| author | Tayyebe Nasri Behrooz Mashayekhy Hanieh Mirebrahimi |
| author_facet | Tayyebe Nasri Behrooz Mashayekhy Hanieh Mirebrahimi |
| author_sort | Tayyebe Nasri |
| collection | DOAJ |
| description | In this paper, we introduce a subcategory ∼Sh* of Sh* and obtain some results in this subcategory. First we show that there is a natural bijection Sh(∑(X, x), (Y,y))≅Sh((X,x),Sh((I, Ī),(Y,y))), for every (Y,y)∈ ~Sh* and (X,x)∈ Sh*. By this fact, we prove that for any pointed topological space (X,x) in ∼Sh*,πntop(X,x)≅ πn-ktop(Sh((Sk, *),(X,x)), ex), for all 1≤k ≤n-1. |
| first_indexed | 2024-03-11T11:13:46Z |
| format | Article |
| id | doaj.art-b65450ea8a6c4c7ebe2850bd53917600 |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:13:46Z |
| publishDate | 2021-03-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-b65450ea8a6c4c7ebe2850bd539176002023-11-11T10:02:49ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652021-03-0161233310.22052/mir.2021.240322.1246111348Adjointness of Suspension and Shape Path FunctorsTayyebe Nasri0Behrooz Mashayekhy1Hanieh Mirebrahimi2Department of Pure Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, IranDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, IranDepartment of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, IranIn this paper, we introduce a subcategory ∼Sh* of Sh* and obtain some results in this subcategory. First we show that there is a natural bijection Sh(∑(X, x), (Y,y))≅Sh((X,x),Sh((I, Ī),(Y,y))), for every (Y,y)∈ ~Sh* and (X,x)∈ Sh*. By this fact, we prove that for any pointed topological space (X,x) in ∼Sh*,πntop(X,x)≅ πn-ktop(Sh((Sk, *),(X,x)), ex), for all 1≤k ≤n-1.https://mir.kashanu.ac.ir/article_111348_a639434f373b5e2c1e63558d731d8772.pdfshape categorytopological shape homotopy groupshape groupsuspensions |
| spellingShingle | Tayyebe Nasri Behrooz Mashayekhy Hanieh Mirebrahimi Adjointness of Suspension and Shape Path Functors Mathematics Interdisciplinary Research shape category topological shape homotopy group shape group suspensions |
| title | Adjointness of Suspension and Shape Path Functors |
| title_full | Adjointness of Suspension and Shape Path Functors |
| title_fullStr | Adjointness of Suspension and Shape Path Functors |
| title_full_unstemmed | Adjointness of Suspension and Shape Path Functors |
| title_short | Adjointness of Suspension and Shape Path Functors |
| title_sort | adjointness of suspension and shape path functors |
| topic | shape category topological shape homotopy group shape group suspensions |
| url | https://mir.kashanu.ac.ir/article_111348_a639434f373b5e2c1e63558d731d8772.pdf |
| work_keys_str_mv | AT tayyebenasri adjointnessofsuspensionandshapepathfunctors AT behroozmashayekhy adjointnessofsuspensionandshapepathfunctors AT haniehmirebrahimi adjointnessofsuspensionandshapepathfunctors |