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## Main Question or Discussion Point

There is a class in my uni called Real Analysis, which covers mostly metric spaces and generally a bunch of slightly more advanced topics than just your basic calculus/multivariable calculus/very basic number theory etc. There are some notes that you can download but for some reason no recommended books so I'm looking for something good.

Here are most of the subjects the class covers to give you a better idea:

Peano axioms, Properties of real and natural numbers, Dedekind cuts, metric space definitions, examples and metrics in vector spaces defined by norms, open and closed subsets of metric spaces, equivalent metrics, countable and uncountable sets, Zorn lemma, metric space completeness, Baire theorem, C[a, b] spaces, Arzela theorem, products of metric spaces, Cantor set etc.

Here are most of the subjects the class covers to give you a better idea:

Peano axioms, Properties of real and natural numbers, Dedekind cuts, metric space definitions, examples and metrics in vector spaces defined by norms, open and closed subsets of metric spaces, equivalent metrics, countable and uncountable sets, Zorn lemma, metric space completeness, Baire theorem, C[a, b] spaces, Arzela theorem, products of metric spaces, Cantor set etc.