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.

I really like Howland's 'Basic Real Analysis'.  The only unfortunate bit is that the topology proofs are in appendices. That said, the book is readable with only basic calculus, and really well-written for the student (rather than as a reference text). 
