We prove that the topological φ-category of a pair (M,N) of topological manifolds is infinite if the algebraic φ-category of the pair of fundamental groups (π₁(M),π₁(N)) is infinite. Some immediate consequences of this fact are also pointed out.
@article{bwmeta1.element.bwnjournal-article-apmv67z1p87bwm,
author = {Cornel Pintea},
title = {Continuous mappings with an infinite number of topologically critical points},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {87-93},
zbl = {0885.57015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z1p87bwm}
}
Cornel Pintea. Continuous mappings with an infinite number of topologically critical points. Annales Polonici Mathematici, Tome 66 (1997) pp. 87-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z1p87bwm/
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