Subject: RE: question From: "Neil Strickland" Date: Thu, 9 Dec 2004 14:03:38 -0000 To: "Don Davis" Let I be the first uncountable ordinal, and for i in I let X(i) be the space of order-preserving embeddings of the ordinal i in the real line, with bounded image. For i < j we have a restriction map X(j) -> X(i), whose fibres are nonempty convex subsets of Map( (i,j], R) and so are contractible. The inverse limit is empty (for if f : I -> R is an order embedding, we can choose a rational number between f(i) and f(i+1) for each i, giving uncountably many rationals). Neil >> From:Dr.George,Adel A. >> >> I have the following question,please post it: >> Let X(i) be an inverse system of contractible >> topological spaces where for j>i the map X(j)--->X(i) >> is a continuous surjection with contractible fibers.I >> wish to show that X(= the inverse limit of the X(i)) >> is nonempty? >> >> Are there some set theoretic conditions that >> insure that an inverse limit is non-empty other than >> the familiar 2 conditions stated in Bourbaki "Set >> Theory"? >> >> Thank you. >> >>