Continuous approximate roots of polynomial equations via shape theory

2025/10/02 by Lau, Joshua, Marin-Marquez, Vicente
#FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.2510.01613

Abstract

We study continuous approximate solutions to polynomial equations over the ring C(X) of continuous complex-valued functions over a compact Hausdorff space X. We show that when X is one-dimensional, the existence of such approximate solutions is governed by the behaviour of maps from the fundamental pro-group of X into braid groups.

Citations

• K-theory of co-existentially closed continua
• A hierarchy of maps between compacta
• On covering dimension and inverse limits of compact spaces

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