Revisiting Cauty's proof of the Schauder conjecture
Dobrowolski, Tadeusz
Abstr. Appl. Anal., Tome 2003 (2003) no. 7, p. 407-433 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
The Schauder conjecture that every compact convex subset of a metric linear space has the fixed-point property was recently established by Cauty (2001). This paper elaborates on Cauty's proof in order to make it more detailed, and therefore more accessible. Such a detailed analysis allows us to show that the convex compacta in metric linear spaces possess the simplicial approximation property introduced by Kalton, Peck, and Roberts. The latter demonstrates that the original Schauder approach to solve the conjecture is in some sense “correctable.”
Publié le : 2003-04-13
Classification:  54H25,  47H10,  55M20,  46A16,  46A55,  46T20,  52A07 
@article{1050425912,
     author = {Dobrowolski, Tadeusz},
     title = {Revisiting Cauty's proof of the Schauder conjecture},
     journal = {Abstr. Appl. Anal.},
     volume = {2003},
     number = {7},
     year = {2003},
     pages = { 407-433},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1050425912}
}

Dobrowolski, Tadeusz. Revisiting Cauty's proof of the Schauder conjecture. Abstr. Appl. Anal., Tome 2003 (2003) no. 7, pp.  407-433. http://gdmltest.u-ga.fr/item/1050425912/