Geodesic
On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 192-204

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

DOI

Let p ≥ 3 be a prime number and m a positive integer, and let S be the sphere S (m-1)(p-1)-1 . Let f:S→S be a map without fixed points and with f p = idS . We show that there exists an h: S→Rm with h(x) ≠ h(f(x)) for all x ∈ S. From this we conclude that there exists a closed cover U 1,..., U 4m of S with U i nf(U i ) = Ø for i = 1,..., 4m. We apply these results to Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk theorems in the framework of the sectional category and to a problem in asymptotic fixed point theory.
DOI : 10.4153/CMB-1984-029-6
Mots-clés : 55M20, 47H10 
Steinlein, H. On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 192-204. doi: 10.4153/CMB-1984-029-6
@article{10_4153_CMB_1984_029_6,
     author = {Steinlein, H.},
     title = {On the {Theorems} of {Borsuk-Ulam} and {Ljusternik-Schnirelmann-Borsuk}},
     journal = {Canadian mathematical bulletin},
     pages = {192--204},
     year = {1984},
     volume = {27},
     number = {2},
     doi = {10.4153/CMB-1984-029-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-029-6/}
}
TY  - JOUR
AU  - Steinlein, H.
TI  - On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk
JO  - Canadian mathematical bulletin
PY  - 1984
SP  - 192
EP  - 204
VL  - 27
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-029-6/
DO  - 10.4153/CMB-1984-029-6
ID  - 10_4153_CMB_1984_029_6
ER  - 
%0 Journal Article
%A Steinlein, H.
%T On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk
%J Canadian mathematical bulletin
%D 1984
%P 192-204
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-029-6/
%R 10.4153/CMB-1984-029-6
%F 10_4153_CMB_1984_029_6

Cité par Sources :