Fix merge issues (old PR - #404) #409
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Used exercise 1.1.18 and the countable union of rationals in [0,1] example to demonstrate an example for exercise 1.2.1. All code has been written by AI (proof sketch was given by me) with occasional human intervention. Mathlib was used for some topological results. I'll rewrite code and reopen the pull request incase this code violates any of the rules of the codebase.