Coordinate axes/Metric space/Exercise

Let $A\subseteq {ℝ}^2$ be the union of the $x$-axis and the $y$-axis.

a) Define the distance on $A$ given by the shortest connection between the two points $P,Q\in A$ by a path on $A$.

b) Show that this is a metric.

c) Does there exist a norm on ${ℝ}^2$ such that the restriction of the corresponding metric coincides with the given connecting metric?

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