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Mathematics

Connectedness: The Topological Idea of Being One Piece

Quick fact

In topology, the interval [0,1] and the circle are both connected, but the circle is not homeomorphic to the interval because removing a point from the interval disconnects it, while removing a point from a circle leaves it connected.

Why this is interesting

Think of a coiled rope and two separate shoelaces. Both look like strings, but one is 'all one piece' and the other is not. How can mathematics capture such a basic difference?

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Connectedness: The Topological Idea of Being One Piece

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