If B(x?, E?) and B(x2, ?) are open balls in (R2, d) where d is the Euclidean metric, and if x3 E B(x?, ?) B(x?, ?); find 3 0 such that B(x3, 3) ? B (x?, ?) B(x?, ?). Let (X, d) be a totally bounded space and A ? X; show that (A, d|A) is totally bounded. Prove that [0, 1) and (0, 1) are equipotent. solutionspile.com

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If B(x?, E?) and B(x2, ?) are open balls in (R2, d) where d is the Euclidean metric, and if x3 E B(x?, ?) B(x?, ?); find 3 > 0 such that B(x3, 3) ? B (x?, ?) B(x?, ?). Let (X, d) be a totally bounded space and A ? X; show that (A, d|A) is totally bounded. Prove that [0, 1) and (0, 1) are equipotent. solutionspile.com

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