Comparison of topologies on fundamental groups with subgroup topology viewpoint
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Naghmeh Shahami
Abstract
In order to make the fundamental group (one of the most well-known invariants in algebraic topology) more useful and powerful, some researchers have introduced and studied various topologies on the fundamental group from the beginning of the 21st century onwards. In this paper, first we recall and review these topologies and then using the concept of subgroup topology, we compare these topologies in order to present some results on topologized fundamental groups.
(Communicated by Tibor Macko)
Acknowledgement
The authors would like to thank the referees for their careful reading and useful comments and suggestions that helped to improve the article.
References
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Articles in the same Issue
- Generalized Sasaki mappings in d0-Algebras
- On a theorem of Nathanson on Diophantine approximation
- Constructing infinite families of number fields with given indices from quintinomials
- Partitions into two Lehmer numbers in ℤq
- Fundamental systems of solutions of some linear differential equations of higher order
- On k-Circulant matrices involving the Lucas numbers of even index
- Explicit formulae for the Drazin inverse of the sum of two matrices
- On nonoscillation of fractional order functional differential equations with forcing term and distributed delays
- Novel generalized tempered fractional integral inequalities for convexity property and applications
- Convergence of α-Bernstein-Durrmeyer operators about a collection of measures
- The problem of finding eigenvalues and eigenfunctions of boundary value problems for an equation of mixed type
- Orbital Hausdorff dependence and stability of the solution to differential equations with variable structure and non-instantaneous impulses
- Improvements on the Leighton oscillation theorem for second-order dynamic equations
- Topogenous orders on forms
- Comparison of topologies on fundamental groups with subgroup topology viewpoint
- An elementary proof of the generalized Itô formula
- Asymptotic normality for kernel-based test of conditional mean independence in Hilbert space
- Advancing reliability and medical data analysis through novel statistical distribution exploration
- Historical notes on the 75th volume of Mathematica Slovaca - Authors of the first issue from 1951
