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

Voir la notice de l'article provenant de la source Cambridge University Press

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
@article{10_4153_CMB_2011_158_8,
     author = {Jacob, Beno{\^\i}t},
     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/}
}
TY  - JOUR
AU  - Jacob, Benoît
TI  - On Perturbations of Continuous Maps
JO  - Canadian mathematical bulletin
PY  - 2013
SP  - 92
EP  - 101
VL  - 56
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-158-8/
DO  - 10.4153/CMB-2011-158-8
ID  - 10_4153_CMB_2011_158_8
ER  - 
%0 Journal Article
%A Jacob, Benoît
%T On Perturbations of Continuous Maps
%J Canadian mathematical bulletin
%D 2013
%P 92-101
%V 56
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-158-8/
%R 10.4153/CMB-2011-158-8
%F 10_4153_CMB_2011_158_8

[1] [1] Choi, M. D. and Elliott, G. A., Density of the selfadjoint elements with finite spectrum in an irrational rotation C*-algebra. Math. Scand. 67 (1990), no. 1, 73-86. Google Scholar

[2] [2] Engelking, R., Dimension theory. North-Holland Mathematical Library, 19, North-Holland Publishing Co., Amsterdam-Oxford-New York; PWN-Polish Scientific Publishers, Warsaw, 1978. Google Scholar

[3] [3] Nagata, J., Modern dimension theory. Revised ed., Sigma Series in Pure Mathematics, 2, Heldermann Verlag, Berlin, 1983. Google Scholar

[4] [4] Phillips, N. C., Simple C*-algebras with the property weak (FU). Math. Scand. 69 (1991), no. 1, 127-151. Google Scholar

[5] [5] Phillips, N. C., How many exponentials? Amer. J. Math. 116 (1994), no. 6, 1513-1543. Google Scholar | DOI

Cité par Sources :