Hacettepe Journal of Mathematics and Statistics, ( ISI ), Volume (49), No (4), Year (2020-12) , Pages (1437-1449)

Title : ( On topological homotopy groups and relation to Hawaiian groups )

Authors: Ameneh Babaee , Behrooz Mashayekhy Fard , Bibi Hanieh Mirebrahimi Paziquee , Hamid Torabi Ardakani , Mehdi Abdullahi Rashid , seyed zeynal pashaei ,

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Abstract

Bygeneralizingthewhiskertopologyonthe nthhomotopygroupofpointedspace(X,x0), denoted by πwh n (X,x0), we show that πwh n (X,x0) is a topological group if n ≥ 2. Also,we present some necessary and sufficient conditions for πwh n (X,x0) to be discrete, Hausdorff and indiscrete. Then we prove that Ln(X,x0) the natural epimorphic image of the Hawaiian group Hn(X,x0) is equal to the set of all classes of convergent sequences to the identity in πwh n (X,x0). As a consequence, we show that Ln(X,x0) ∼ = Ln(Y,y0) if πwh n (X,x0)∼ = πwh n (Y,y0), buttheconversedoesnotholdingeneral, exceptforsomeconditions. Also,weshowthatonsomeclassesofspacessuchassemilocally n-simplyconnected spaces and n-Hawaiian like spaces, the whisker topology and the topology induced by the compact-open topology of n-loop space coincide. Finally, we show that n-SLT paths can transfer πwh n and hence Ln isomorphically along its points.

Keywords

, Whisker topology, Hawaiian group, n-dimensional Hawaiian earring, harmonic archipelago
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@article{paperid:1080741,
author = {Babaee, Ameneh and Mashayekhy Fard, Behrooz and Mirebrahimi Paziquee, Bibi Hanieh and Torabi Ardakani, Hamid and Abdullahi Rashid, Mehdi and Pashaei, Seyed Zeynal},
title = {On topological homotopy groups and relation to Hawaiian groups},
journal = {Hacettepe Journal of Mathematics and Statistics},
year = {2020},
volume = {49},
number = {4},
month = {December},
issn = {1303-5010},
pages = {1437--1449},
numpages = {12},
keywords = {Whisker topology; Hawaiian group; n-dimensional Hawaiian earring; harmonic archipelago},
}

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%0 Journal Article
%T On topological homotopy groups and relation to Hawaiian groups
%A Babaee, Ameneh
%A Mashayekhy Fard, Behrooz
%A Mirebrahimi Paziquee, Bibi Hanieh
%A Torabi Ardakani, Hamid
%A Abdullahi Rashid, Mehdi
%A Pashaei, Seyed Zeynal
%J Hacettepe Journal of Mathematics and Statistics
%@ 1303-5010
%D 2020

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