On subgroup topologies on fundamental groups

Objective & Hypothesis:It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group.

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Key Findings & Data: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.

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Conclusion & Impact:Moreover, we provide some examples of topological spaces to compare topologies of fundamental groups.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Semicovering · Generalized covering · Topological group

Abstract

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.

Keywords

Semicovering Generalized covering Topological group Spanier topology Whisker topology Lasso topology Subgroup topology

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Cite This Article

Rashid, M. A., Jamali, N., Mahsayekhy, B., Pashaei, S. Z., Torabı, H. (2020). On subgroup topologies on fundamental groups. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 3. https://doi.org/10.15672/hujms.464056

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