# Describe the relative topology of the unit circle as a subspace of the plane

A question from Dugundji's book which I don't even understand the statement.

Describe the relative topology of $\{z: |z|=1\}$ as a subspace of ${\mathbb{R}}^{2}$.

What do they mean by "describe"? I don't understand what they are asking for. Can you please clarify?

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I don't know what describe means either. The open sets are countable unions of disjoint open arcs; that's one way to describe the topology. It's a compact connected 1-dimensional manifold (the only one up to homeomorphism). –  Jonas Meyer Dec 22 '10 at 6:30