Question 4: Suppose that the metric d on M is the discrete metric. (a) Show that every map f: M →Y is continuous. (b) Show that if M = R", then the map Id: (R", d) → R" : 1+I is uniformly continuous. (recall that when no metric is specified on R", its standard metric is assumed. Also, d is clearly the discrete metric.)

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Question 4: Suppose that the metric d on M is the discrete metric.
(a) Show that every map f: M →Y is continuous.
(b) Show that if M = R", then the map Id: (R", d) → R": r+ x is uniformly
continuous. (recall that when no metric is specified on R", its standard
metric is assumed. Also, d is clearly the discrete metric.)
Transcribed Image Text:Question 4: Suppose that the metric d on M is the discrete metric. (a) Show that every map f: M →Y is continuous. (b) Show that if M = R", then the map Id: (R", d) → R": r+ x is uniformly continuous. (recall that when no metric is specified on R", its standard metric is assumed. Also, d is clearly the discrete metric.)
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