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Topological fundamental groups and small generated coverings

In: Mathematica Slovaca, vol. 65, no. 5
Hamid Torabi - Ali Pakdaman - Behrooz Mashayekhy

Details:

Year, pages: 2015, 1153 - 1164
Keywords:
quasitopological fundamental group, topological fundamental group, SG subgroup, small generated covering, semi-locally small generated space
About article:
This paper is devoted to study some topological properties of the SG subgroup $π1sg(X,x)$ of the quasitopological fundamental group of a based space $(X,x)$, $\pt$, its topological properties as a subgroup of the topological fundamental group $π1τ(X,x)$ and its influence on the existence of universal covering of $X$. First, we introduce small generated spaces which have indiscrete topological fundamental groups and also small generated coverings which are universal coverings in the categorical sense. Second, we give a necessary and sufficient condition for the existence of the small generated coverings. Finally, by introducing the notion of semi-locally small generatedness we show that the quasitopological fundamental groups of semi-locally small generated spaces are topological groups.
How to cite:
ISO 690:
Torabi, H., Pakdaman, A., Mashayekhy, B. 2015. Topological fundamental groups and small generated coverings. In Mathematica Slovaca, vol. 65, no.5, pp. 1153-1164. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0079

APA:
Torabi, H., Pakdaman, A., Mashayekhy, B. (2015). Topological fundamental groups and small generated coverings. Mathematica Slovaca, 65(5), 1153-1164. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0079
About edition:
Published: 1. 10. 2015