Proof No. 4 Please prove in the same style as No. 3

Continuous We prove that is Continous by wing here: e Continues on X basic open sel wsy, f(w) is open in X let W be ang basic open set in 21,00) I basic open set in (12 a) is (a, b) such that W = (a,h) [1,00) OR 77 We have two cases: Case 1. We can, where Isacb. Sina Isach 38(w) - f ( (a, b) (tit) (1 t) open in (0,1) as (tit) - (hitos Case 2: W = [1, b) where Kb. Seet (1) 8(W) - P1 [, b) = (t 1] (t. 1 open in Lo, 1] (4611] = (1, 142 0(0, 1] 3 f Continuous > 4 e Continums. pic, (01) defined by f(x) = V[1,-) Continuous We prove that is Continous by wing here: e Continues on X basic open sel wsy, f(w) is open in X let W be ang basic open set in 21,00) I basic open set in (12 a) is (a, b) such that W = (a,h) [1,00) OR 77 We have two cases: Case 1. We can, where Isacb. Sina Isach 38(w) - f ( (a, b) (tit) (1 t) open in (0,1) as (tit) - (hitos Case 2: W = [1, b) where Kb. Seet (1) 8(W) - P1 [, b) = (t 1] (t. 1 open in Lo, 1] (4611] = (1, 142 0(0, 1] 3 f Continuous > 4 e Continums. pic, (01) defined by f(x) = V[1,-)