Basic Analysis I — Real Analysis · Problem 7.1.11

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · metric-spaces

Problem

a) Find a metric dd on N\mathbb{N} such that N\mathbb{N} is an unbounded set in (N,d)(\mathbb{N}, d). b) Find a metric dd on N\mathbb{N} such that N\mathbb{N} is a bounded set in (N,d)(\mathbb{N}, d). c) Find a metric dd on N\mathbb{N} such that for every n∈Nn \in \mathbb{N} and every ϵ>0\epsilon > 0, there exists an m∈Nm \in \mathbb{N} such that d(n,m)<ϵd(n,m) < \epsilon.

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