It is proved, for various spaces A, such as a surface of genus 2, a figure-eight, or a sphere of dimension ≠ 1,3,7, and for any set Σ of equations, that Σ cannot be modeled by continuous operations on A unless Σ is undemanding (a form of triviality that is defined in the paper).
@article{bwmeta1.element.bwnjournal-article-fmv164i3p193bwm,
author = {Walter Taylor},
title = {Spaces and equations},
journal = {Fundamenta Mathematicae},
volume = {163},
year = {2000},
pages = {193-240},
zbl = {0968.08004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv164i3p193bwm}
}
Taylor, Walter. Spaces and equations. Fundamenta Mathematicae, Tome 163 (2000) pp. 193-240. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv164i3p193bwm/
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