Geodesic
On Perturbations of Continuous Maps
Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 92-101

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DOI

We give sufficient conditions for the following problem: given a topological space $X$ , a metric space $Y$ , a subspace $Z$ of $Y$ , and a continuous map $f$ from $X$ to $Y$ , is it possible, by applying to $f$ an arbitrarily small perturbation, to ensure that $f\left( {{X}^{'}} \right)$ does not meet $Z$ ? We also give a relative variant: if $f\left( X\prime\right)$ does not meet $Z$ for a certain subset ${X}'\subset X$ , then we may keep $f$ unchanged on ${X}'$ . We also develop a variant for continuous sections of fibrations and discuss some applications to matrix perturbation theory.
DOI : 10.4153/CMB-2011-158-8
Mots-clés : 54F45, perturbation theory, general topology, applications to operator algebras / matrix perturbation theory 
Jacob, Benoît. On Perturbations of Continuous Maps. Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 92-101. doi: 10.4153/CMB-2011-158-8
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     title = {On {Perturbations} of {Continuous} {Maps}},
     journal = {Canadian mathematical bulletin},
     pages = {92--101},
     year = {2013},
     volume = {56},
     number = {1},
     doi = {10.4153/CMB-2011-158-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-158-8/}
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