Macroeconomics Exam Review 9

Macroeconomics Exam Review 9 - 1 2 1 1 / 2 ((2 , 0)) Figure...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 2 1 1 / 2 ((2 , 0)) Figure 1.2: Open ball about (2 , 0) relative to 1.95 Assume is connected. Suppose is not an interval. This implies that there exists numbers ,, such that < < and , while / . Then = ( ( , )) ( ( , )) represents as the union of two disjoint open sets (relative to ), contradicting the assumption that is connected. Conversely, assume that is an interval. Suppose that is not connected. That is, = where and are nonempty disjoint closed sets. Choose and . Since and are disjoint, = . Without loss of generality, we may assume < . Since is an interval, [ , ] = . Let = sup { [ , ] } Clearly so that . Now belongs to either or . Since....
View Full Document

This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.

Ask a homework question - tutors are online