Real analysis book suggestion I am searching for a real analysis book (instead of Rudin's) which satisfies the following requirements:


*

*clear, motivated (but not chatty), clean exposition in definition-theorem-proof style;

*complete (and possibly elegant and explicative) proofs of every theorem;

*examples and solved exercises;

*possibly, the proofs of the theorems on limits of functions should not use series;

*generalizations of theorem often given for $\mathbb{R}$ to metric spaces and also to topological spaces.


Thank you very much in advance for your assistance.

Analysis 1 and Analysis 2 by Terence Tao.
