Revisiting Cauty′s proof of the Schauder conjecture

Tadeusz Dobrowolski

Abstract and Applied Analysis, 2003, vol. 2003, issue 7, 407-433

Abstract: 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.”

Date: 2003
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/S1085337503211015

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2003:y:2003:i:7:p:407-433

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().