On construit un simplexe de Choquet dont l’ensemble des points extrémaux est -analytique, mais n’est pas -Borélien. L’ensemble est un dans sa compactification de Stone-Cech. C’est donc un exemple d’ensemble qui n’est pas absolu.
We construct a Choquet simplex whose set of extreme points is -analytic, but is not a -Borel set. The set has the surprising property of being a set in its Stone-Cech compactification. It is hence an example of a set that is not absolute.
@article{AIF_1985__35_3_195_0, author = {Talagrand, Michel}, title = {Choquet simplexes whose set of extreme points is $K$-analytic}, journal = {Annales de l'Institut Fourier}, pages = {195--206}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {35}, number = {3}, year = {1985}, doi = {10.5802/aif.1024}, zbl = {0564.46008}, mrnumber = {87a:46022}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1024/} }
TY - JOUR AU - Talagrand, Michel TI - Choquet simplexes whose set of extreme points is $K$-analytic JO - Annales de l'Institut Fourier PY - 1985 DA - 1985/// SP - 195 EP - 206 VL - 35 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1024/ UR - https://zbmath.org/?q=an%3A0564.46008 UR - https://www.ams.org/mathscinet-getitem?mr=87a:46022 UR - https://doi.org/10.5802/aif.1024 DO - 10.5802/aif.1024 LA - en ID - AIF_1985__35_3_195_0 ER -
Talagrand, Michel. Choquet simplexes whose set of extreme points is $K$-analytic. Annales de l'Institut Fourier, Tome 35 (1985) no. 3, pp. 195-206. doi : 10.5802/aif.1024. http://www.numdam.org/articles/10.5802/aif.1024/
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