I have heard about KKM (Knaster-Kuratowski-Mazurkiewicz) theorem in nonlinear analysis and I am trying to use that for a theorem I am working on. The original paper (1929) is in German and all the references I have found on the Net mainly deal with generalizations of this theorem or present the theorem with a lot of complex topological flavor. I was wondering if anybody knows a source which contains this theorem in its basic format.
There is a book devoted entirely to KKM theory and its applications. It contains an outline of the classical KKM theorem as well as a number of generalizations. Another standard reference is "Fixed point theory" by Granas and Dugundji.