Is there a general book of mathematics which starts from first order logic, treats set theory (in ZF setting) in which first order logic is used, then abstract algebra (in which set theory is heavily used), topology (at least point set topology) and finally mathematical analysis (in which all the previous concepts are used). In all these parts most important results should be covered.

In this way one can study mathematical analysis having solid foundations of mathematics? Am I dreaming or a book of this kind exists?

  • 2
    $\begingroup$ Hardly. Each one one these topics requires at least one book, if not more depending on where you set the limits. Abstract algebra, topology, and analysis are huge areas. $\endgroup$ Aug 29 at 15:03
  • 4
    $\begingroup$ Sounds like an awful book. $\endgroup$
    – Randall
    Aug 29 at 15:03
  • $\begingroup$ It is not a dream to study analysis having solid knowledge of the foundations of mathematics, but you'd probably have to read different books, one for each subject. $\endgroup$
    – Manlio
    Aug 29 at 15:18
  • $\begingroup$ Evan Chen's Infinitely Long Napkin, is the closest to what you seek (you can find it online pretty easily). Also, Princeton Companion to Mathematics is a dictionary of sorts. There's also "All the Math You Missed, but Need to Know for Graduate School", by Thomas A. Garrity. $\endgroup$
    – algebroo
    Aug 29 at 15:26
  • $\begingroup$ Hopefully not... $\endgroup$ Aug 29 at 16:12

1 Answer 1


Check out Schechter's Handbook of Analysis and its Foundations, if you can find a copy. :)


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