This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: x * , there is an open segment of the line that (a) contains x * and (b) is a subset of A . The length of the segment can depend on the line. The property of being internal is related to, but distinct from, the property of being interior . Recall that if ( X,d ) is a metric space and A X , then x * is interior to A i there is an > 0 such that N ( x ) A . (a) Provide an example in R 2 of a set A and a point x * such that x * is internal to A but not interior to A . A picture with a clear accompanying explanation is ideal. (b) Prove that if x * is interior to A R N then it is internal to A . (c) Consider ( R ,d p ), where d p is the pointwise convergence metric. Is the point (1 , 1 ,... ) internal to R + ? If yes, provide a proof; if no, provide a concrete, clear counterexample....
View
Full
Document
This note was uploaded on 05/20/2010 for the course ECON 511 taught by Professor Johnnachbar during the Fall '08 term at Washington University in St. Louis.
 Fall '08
 JohnNachbar
 Economics

Click to edit the document details