I have seen a lot of suggestions of real analysis textbooks on StackExchange. But unfortunately, because my university course (I am in undergraduate year 2) does not teach Topology before Analysis, the exercises in classics like Rudin and Apostol could be impregnable to me.
Do you have any suggestion of problem books for undergraduate real analysis? They don't need to be dedicated problem books, any book that has many exercises would do. The level of difficulty of the exercises should be at least the level of those in Apostol's "Mathematical analysis". Most importantly, Topology is not needed to solve the book's problems.
Here are the topics I want to cover:
Riemann integrals: Proving functions are Riemann integrable, and properties of Riemann sums and integrals
Uniform continuity & Uniform convergence: Proving functions are uniformly continuous/convergent, and properties of uniformly continuous/convergent functions