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Mathematics

Topology of the Real Line: Open and Closed Sets

Quick fact

The empty set and the entire real line are both open and closed—they are 'clopen' sets, a fact that surprises many newcomers to topology.

Why this is interesting

You’ve probably heard of 'open' and 'closed' doors, but did you know that mathematicians use these words to describe points on a line—with a surprisingly strict rule? What if a set could be both open and closed at the same time?