On Topological Shape Homotopy Groups
نویسنده:
, , , , , , ,سال
: 2016
چکیده: In this paper, using the topology on the set of shape morphisms between arbitrary topological spaces $X$,
$Y$, $Sh(X,Y)$, defined by Cuchillo-Ibanez et al. in 1999, we consider a topology on the shape homotopy groups of arbitrary topological spaces, which make them Hausdorff topological groups. We then exhibit an example in which $\\check{\\pi}_k^{top}$ succeeds in distinguishing the shape type of $X$ and $Y$ while $\\check{\\pi}_k$ fails, for all $k\\in \\Bbb{N}$. Moreover, we present some basic properties of topological shape homotopy groups, among them commutativity of $\\check{\\pi}_k^{top}$ with finite product of compact Hausdorff spaces. Finally, we consider a quotient topology on the $k$th shape group, induced by the $k$th shape loop space and show that it coincides with the above topology.
$Y$, $Sh(X,Y)$, defined by Cuchillo-Ibanez et al. in 1999, we consider a topology on the shape homotopy groups of arbitrary topological spaces, which make them Hausdorff topological groups. We then exhibit an example in which $\\check{\\pi}_k^{top}$ succeeds in distinguishing the shape type of $X$ and $Y$ while $\\check{\\pi}_k$ fails, for all $k\\in \\Bbb{N}$. Moreover, we present some basic properties of topological shape homotopy groups, among them commutativity of $\\check{\\pi}_k^{top}$ with finite product of compact Hausdorff spaces. Finally, we consider a quotient topology on the $k$th shape group, induced by the $k$th shape loop space and show that it coincides with the above topology.
کلیدواژه(گان): Topological shape homotopy group\\sep Shape group\\sep Topological group\\sep Inverse limit
کالکشن
:
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آمار بازدید
On Topological Shape Homotopy Groups
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contributor author | طیبه نصری | en |
contributor author | فاطمه قانعی | en |
contributor author | بهروز مشایخی فرد | en |
contributor author | بی بی هانیه میر ابراهیمی پازیکوئی | en |
contributor author | tayyebe nasri | fa |
contributor author | fateme ghanei | fa |
contributor author | Behrooz Mashayekhy Fard | fa |
contributor author | Bibi Hanieh Mirebrahimi Paziquee | fa |
date accessioned | 2020-06-06T13:26:47Z | |
date available | 2020-06-06T13:26:47Z | |
date issued | 2016 | |
identifier uri | http://libsearch.um.ac.ir:80/fum/handle/fum/3355163 | |
description abstract | In this paper, using the topology on the set of shape morphisms between arbitrary topological spaces $X$, $Y$, $Sh(X,Y)$, defined by Cuchillo-Ibanez et al. in 1999, we consider a topology on the shape homotopy groups of arbitrary topological spaces, which make them Hausdorff topological groups. We then exhibit an example in which $\\check{\\pi}_k^{top}$ succeeds in distinguishing the shape type of $X$ and $Y$ while $\\check{\\pi}_k$ fails, for all $k\\in \\Bbb{N}$. Moreover, we present some basic properties of topological shape homotopy groups, among them commutativity of $\\check{\\pi}_k^{top}$ with finite product of compact Hausdorff spaces. Finally, we consider a quotient topology on the $k$th shape group, induced by the $k$th shape loop space and show that it coincides with the above topology. | en |
language | English | |
title | On Topological Shape Homotopy Groups | en |
type | Journal Paper | |
contenttype | External Fulltext | |
subject keywords | Topological shape homotopy group\\sep Shape group\\sep Topological group\\sep Inverse limit | en |
journal title | Topology and its Applications | fa |
pages | 22-33 | |
journal volume | 198 | |
journal issue | 1 | |
identifier link | https://profdoc.um.ac.ir/paper-abstract-1052799.html | |
identifier articleid | 1052799 |