On The Whisker Topology

2024/11/26 by John K. Aceti, Aceti, John K.
Economics, Econometrics and Finance · Social Sciences · #55P10 #Algebraic Topology (math.AT) #Economic Theory and Policy #FOS: Mathematics #General Topology (math.GN) #Housing, Finance, and Neoliberalism #Political Economy and Marxism

paper · pdf · doi:10.48550/arxiv.2412.05304

openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to explore properties of the whisker topology, which is a topology endowed on the fundamental group and whose utility is to detect locally complicated phenomena in pathological topological spaces. We show that the whisker topology preserves products, resolve an open question regarding the existence of a space which makes π₁^wh(X,x₀) a non-discrete, non-abelian, and Hausdorff topological group, and show the whisker topology is not separable on the earring group π₁(\Er¹,x₀).

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