problem 1 let fr-gtr be a function fxx if xgt0

Question

Problem 1: Let f:R->R be a function f(x)={x, if x>=0 x-1, if x<0

Evaluate whether f is

a) U-U continuous.

b) C-C continuous.

Problem 2: Show that the function d((x₁,y₁), (x₂,y₂)) = |x₁-x₂| + |y₁-y₂| is a metric on R². Evaluate what B₁(0,0)

Problem 3. for any set A in a topological space X. show that

a) Cl(Int(Cl(Int A)))=Cl(Int A)

b) Int(Cl(Int(Cl A)))=Int(Cl A)

*Use properties of interior an closure.