Econ511-WTK-2008Mid - 4111 R N Notes Theorem 4 ( R N is...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Econ 511 Professor: John Nachbar Fall 2008 Required Theorems for 511 Midterm The following is a list of theorems that may appear as test questions. You should be able to prove any one of these. Note that some results are from the 4111 notes and some from the 511 notes. This is not an exhaustive list of important results. 4111 Metric Space Notes Theorem 5 (Convergent sequences are Cauchy) Theorem 6 (Cauchy sequences with a convergent subsequence are convergent) Theorem 7 (A set is open iff every point is interior) Theorem 11 (3 equivalent characterizations of closedness) 4111 Compactness Notes Theorem 1 (Sequentially compact equivalent to complete and totally bounded)
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 4111 R N Notes Theorem 4 ( R N is complete, using previously proved theorems) Theorem 6 (Heine-Borel, again using previously proved theorems) 4111 R Notes Theorem 6 (Examples that bounded sets in R need not be totally bounded) 511 Continuity Notes Theorem 4 (Equivalence of the - and sequence denitions of continuity) 511 Continuity and Connectedness Notes Theorem 2 (Intermediate Value Theorem) 4111 Existence of Optima Notes Theorem 1(the continuous image of a compact set is compact) Theorem 2 (a continuous real-valued function on a compact set has a maxi-mum)...
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.

Ask a homework question - tutors are online