A remark about critical sets in R³

2016/10/06 by Souto, Juan
#26B99 #57M30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1610.01979

Abstract

We give a necessary condition for a closed subset of R³ to be the set of critical points of some smooth function. In particular we obtain that for example neither the Whitehead continuum nor the p-adic solenoid are such a critical sets.

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