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A metric $d: X \times X \to [0,\infty)$ is said to be intrinsic provided that the distance between any two points is the infimum of the lengths of paths joining the points. A space is an inner metric ...

Let the unit arc be, $$\{x \in \mathbb{R}^2| x_1^2 + x_2^2 =1, x_1 \geq 0, x_2 \geq 0\}$$ There is something I found curious about the unit arc which is that, It has an empty interior viewed as a ...