Krantz Steven G. Real Analysis and Foundations

2nd edition. - CRC Press, 2005. - 472p.The book Real Analysis and Foundations, first published in 1991, is
unique in several ways. It was the first book to attempt a bridge between
the rather hard-edged classical books in the subject—like Walter Rudin's
Principles of Mathematical Analysis—and the softer and less rigorousX
books of today. This book combines authority, rigor, and readability
in a manner that makes the subject accessible to students while still
teaching them the strict discourse of mathematics.