Local, Global, and Beyond

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If you look at mathematics literature, particularly in geometry and topology, you’ll see the words ‘local’ and ‘global’ showing up all the time, but they have a completely different meaning to the way that they’d be used in, say, economics literature, or sociology literature, where obviously ‘global’ refers to the entire planet and local to a smaller region of that. These words have been adopted by mathematicians and applied in much more abstract ways to different types of spaces which aren’t necessarily anything like a globe…