There is a class in my uni called Real Analysis, which comes after 3 semesters of "analysis" and 1 semester of complex analysis. I am looking for good books that cover the material, but most of the books I can find are either more basic and cover mostly material that we learned in previous classes or too specialized and intended for graduate students.
Here's some of the topics covered by the class to be more specific: 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.
