# For each set s below prove that s is not compact by

• No School
• AA 1
• uthinkuknowmeee
• 12
• 100% (1) 1 out of 1 people found this document helpful

This preview shows page 12 out of 12 pages.

5. For each setSbelow, prove thatSis not compact by finding an open cover ofSwhich has no finite subcover. Be precise when describing/defining this opencover.(a)S={-1,-4,-9,-16, . . . ,-n2, . . .}.LetG={Gn|nZ+}whereGn= (-n2-1,0).Gis an open cover ofSsinceS[n=1Gn= (-∞,0).However,Ghasno finite subcover, since a finite collection of bounded sets cannot cover anunbounded set.(b)S= [1,2).).