# Totally Bounded : Let M1 be a totally bounded metric space, and f: M1 --> M2 is uniformly continuous and onto. Show M2 is totally bounded.

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6. Let M1 be a totally bounded metric space, and f: M1 --> M2 is uniformly continuous and onto. Show M2 is totally bounded.

Note: we are using the "Methods of Real Analysis by Richard R Goldberg"

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Totally bounded functions are investigated. The solution is detailed and well presented.

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Proof:

First, Since is uniformly continuous, ...

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