Real analysis book suggestion

Analysis 1 and Analysis 2 by Terence Tao.

Mathematical Analysis by Tom M Apostol

I recommend a combination of books Real Mathematical Analysis (Undergraduate Texts in Mathematics) by Charles C. Pugh together with Elementary Classical Analysis by Jerrold E. Marsden, Michael J. Hoffman.These books are concise, motivate the theorems are an elegant presentation.But do not introduce topological spaces.

I believe the book that will satisfy all the requirements of the question will be: Analysis I and Analysis II written by Vladimir A. Zorich. This book has the disadvantage of having an encyclopedic character.

The Zorich's book brings the generalizations of theorem is often do given to $\mathbb{R}$ to metric spaces and topological spaces also to.