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Problem 1 let fr-gtr be a function fxx if xgt0 x-1 if

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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.

Reference no: EM13348003

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