Geodesic
Sets invariant under projections onto one dimensional subspaces
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 227-232

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The Hahn--Banach theorem implies that if $m$ is a one dimensional subspace of a t.v.s. $E$, and $B$ is a circled convex body in $E$, there is a continuous linear projection $P$ onto $m$ with $P(B)\subseteq B$. We determine the sets $B$ which have the property of being invariant under projections onto lines through $0$ subject to a weak boundedness type requirement.
Classification : 46A55, 52A07, 52A10
Keywords: convex; projection; Hahn--Banach; subsets of $\Bbb R^2$ 
@article{CMUC_1991__32_2_a3,
     author = {Fitzpatrick, Simon and Calvert, Bruce},
     title = {Sets invariant under projections onto one  dimensional subspaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {227--232},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {1991},
     mrnumber = {1137783},
     zbl = {0756.52002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a3/}
}
TY  - JOUR
AU  - Fitzpatrick, Simon
AU  - Calvert, Bruce
TI  - Sets invariant under projections onto one  dimensional subspaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1991
SP  - 227
EP  - 232
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a3/
LA  - en
ID  - CMUC_1991__32_2_a3
ER  - 
%0 Journal Article
%A Fitzpatrick, Simon
%A Calvert, Bruce
%T Sets invariant under projections onto one  dimensional subspaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 1991
%P 227-232
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a3/
%G en
%F CMUC_1991__32_2_a3
Fitzpatrick, Simon; Calvert, Bruce. Sets invariant under projections onto one  dimensional subspaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 227-232. http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a3/