3.1 Show that a finite intersection of closed sets is closed. 3.2 Prove that in any metric space (Sd) every open ball S(x) is an open set 3.3 Show that every point of R is zero distance from Q. 3.4...

Extracted text: 3.1 Show that a finite intersection of closed sets is closed. 3.2 Prove that in any metric space (Sd) every open ball S(x) is an open set 3.3 Show that every point of R is zero distance from Q. 3.4 Prove thatif Gis an open set dense in the metric space (S) then S-Gis nowhere dense in S 3.5 Prove that if G,is an open set which is dense in the complete metric space (Sd) is dense in S. 3.6 Is the set S= [0,1] with the discrete metric dseparable? Explain. for n= 1,2,. then