Year 2020, Volume 49 , Issue 3, Pages 935 - 949 2020-06-02

On subgroup topologies on fundamental groups

Mehdi Abdullahi RASHİD [1] , Noorollah JAMALİ [2] , Behrooz MAHSAYEKHY [3] , Seyyed Zeynal PASHAEİ [4] , Hamid TORABI [5]


It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental group and use them to classify coverings, semicoverings, and generalized coverings of a topological space. To do this, we use the concept of subgroup topology on a group and discuss their properties. In particular, we explore which of these topologies make the fundamental group a topological group. Moreover, we provide some examples of topological spaces to compare topologies of fundamental groups.
Semicovering, Generalized covering, Topological group, Spanier topology, Whisker topology, Lasso topology, Subgroup topology
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0001-7222-3922
Author: Mehdi Abdullahi RASHİD
Institution: Ferdowsi University of Mashhad
Country: Iran


Orcid: 0000-0002-3811-1721
Author: Noorollah JAMALİ
Institution: Ferdowsi University of Mashhad
Country: Iran


Orcid: 0000-0001-5243-0641
Author: Behrooz MAHSAYEKHY
Institution: Ferdowsi University of Mashhad
Country: Andorra


Orcid: 0000-0001-7401-6599
Author: Seyyed Zeynal PASHAEİ
Institution: Ferdowsi University of Mashhad
Country: Iran


Orcid: 0000-0002-2609-4872
Author: Hamid TORABI (Primary Author)
Institution: Ferdowsi University of Mashhad
Country: Iran


Dates

Publication Date : June 2, 2020

Bibtex @research article { hujms464056, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {935 - 949}, doi = {10.15672/hujms.464056}, title = {On subgroup topologies on fundamental groups}, key = {cite}, author = {Rashi̇d, Mehdi Abdullahi and Jamali̇, Noorollah and Mahsayekhy, Behrooz and Pashaei̇, Seyyed Zeynal and Torabı, Hamid} }
APA Rashi̇d, M , Jamali̇, N , Mahsayekhy, B , Pashaei̇, S , Torabı, H . (2020). On subgroup topologies on fundamental groups . Hacettepe Journal of Mathematics and Statistics , 49 (3) , 935-949 . DOI: 10.15672/hujms.464056
MLA Rashi̇d, M , Jamali̇, N , Mahsayekhy, B , Pashaei̇, S , Torabı, H . "On subgroup topologies on fundamental groups" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 935-949 <https://dergipark.org.tr/en/pub/hujms/issue/54699/464056>
Chicago Rashi̇d, M , Jamali̇, N , Mahsayekhy, B , Pashaei̇, S , Torabı, H . "On subgroup topologies on fundamental groups". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 935-949
RIS TY - JOUR T1 - On subgroup topologies on fundamental groups AU - Mehdi Abdullahi Rashi̇d , Noorollah Jamali̇ , Behrooz Mahsayekhy , Seyyed Zeynal Pashaei̇ , Hamid Torabı Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.464056 DO - 10.15672/hujms.464056 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 935 EP - 949 VL - 49 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.464056 UR - https://doi.org/10.15672/hujms.464056 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On subgroup topologies on fundamental groups %A Mehdi Abdullahi Rashi̇d , Noorollah Jamali̇ , Behrooz Mahsayekhy , Seyyed Zeynal Pashaei̇ , Hamid Torabı %T On subgroup topologies on fundamental groups %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 3 %R doi: 10.15672/hujms.464056 %U 10.15672/hujms.464056
ISNAD Rashi̇d, Mehdi Abdullahi , Jamali̇, Noorollah , Mahsayekhy, Behrooz , Pashaei̇, Seyyed Zeynal , Torabı, Hamid . "On subgroup topologies on fundamental groups". Hacettepe Journal of Mathematics and Statistics 49 / 3 (June 2020): 935-949 . https://doi.org/10.15672/hujms.464056
AMA Rashi̇d M , Jamali̇ N , Mahsayekhy B , Pashaei̇ S , Torabı H . On subgroup topologies on fundamental groups. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 935-949.
Vancouver Rashi̇d M , Jamali̇ N , Mahsayekhy B , Pashaei̇ S , Torabı H . On subgroup topologies on fundamental groups. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 935-949.

Authors of the Article
Mehdi Abdullahi RASHİD [1]
Noorollah JAMALİ [2]
Behrooz MAHSAYEKHY [3]
Seyyed Zeynal PASHAEİ [4]