2.. (X, d) be the metric space X = 01 with e1(.1,9)= sup(If (x)…


2.. (X, d) be the metric distance X = 01 delay e1(.1,9)= sup(If (x)— 9(2)1: I-1,111. (a) le X finished? Prove your apology. (b) Is X alike? Prove your apology. (c) le X conglomerate? Prove your apology. (d) Is X distinguishable? Prove your apology. 3. (a) Define: It: X m Y is a homeommphism. (b) Define: : X is an isometry. Let Y = C10,11 and d'(),9)=.uallf(z)-9(x)1 : x E [0,11/. (6) IS ,d) homeomorphic to (X, d) defined in tenor 2? (d) Is (Y, d) isometric to (X, d)?

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