Question 2 Which of the following are true or false? If false, give examples. If true, motivate why they are true. (a) Let D C R be open and f : D → R° be continuous. Let G C Rº be open and connected....

#2 need a b c d e f g true or false with explanation
0. Then there is a polynomial P such that for all x € [a, b] , |f (1) – P (r)| < e.="" (g)="" let="" a="" be="" a="" non-empty="" connected="" subset="" of="" the="" cantor="" set.="" then="" a="" consists="" of="" just="" a="" single="" point.="" "/="">
Extracted text: Question 2 Which of the following are true or false? If false, give examples. If true, motivate why they are true. (a) Let D C R be open and f : D → R° be continuous. Let G C Rº be open and connected. Then f-1 (G) is open and connected. (b) Let D = {z € R" : |r|| < 1}.="" let="" f="" :="" d="" →="" r°="" be="" continuous.="" then="" f="" (d)="" contains="" all="" its="" cluster="" points.="" (c)="" let="" d="{r" €="" r"="" :="" ||-||="">< 1}="" u="" {z="" €="" r"="" :="">< ||r||="">< 2}.="" let="" f="" :="" d→="" r°="" be="" continuous.="" then="" f="" (d)="" is="" disconnected.="" (d)="" let="" a,="" c="" r'="" for="" j="" 2="" 1.="" if="" g="" is="" a="" cluster="" point="" of="" ua,="" then="" it="" is="" a="" cluster="" j="1" point="" of="" a,="" for="" at="" least="" one="" j.="" (e)="" let="" {f.="" :="" a="" €="" i}="" be="" a="" collection="" of="" closed="" subsets="" of="" r".="" then="" r"\n="" f.="" contains="" only="" its="" interior="" points.="" (f)="" let="" f="" :="" [a,="" b]="" →="" r="" be="" a="" strictly="" increasing="" function="" (so="" that="" r="">< y="f" (1)="">< f="" (y)).="" let="" e=""> 0. Then there is a polynomial P such that for all x € [a, b] , |f (1) – P (r)| < e.="" (g)="" let="" a="" be="" a="" non-empty="" connected="" subset="" of="" the="" cantor="" set.="" then="" a="" consists="" of="" just="" a="" single="">