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Thanks to my university I have access to all Springer math books. Because of this I have tried to separate some books from Springer to learn the following subjects well (when I say well I refer to a book that requires as a prerequisite only subjects in the undergraduate level, for example, real analysis and that delves deep in the subject that it approaches):

  • Analysis
  • Metric Spaces
  • Multivariate Calculus
  • Topology of Metric Spaces

I have seen that the books "Analysis I", "Analysis II" and "Analysis III", written by Herbert Amann, teaches all these subjects, so I decided to read them. However, I have found other books, the ones listed below, for example, which better teach some subjects addressed by the Herbert Amann books.

The books to which I referred:

  • "Calculus on Normed Vector Spaces", written by Rodney Coleman
  • "Multivariate Calculus and Geometry", written by Seán Dineen
  • "Integration - A Functional Approach", written by Klaus Bichteler
  • "Topologies and Uniformities", written by I.M. James.

All of these books only require the prerequisites I have:

  • Real Analysis
  • Topology of the real line
  • Linear Algebra
  • Abstract Algebra(rings)

Please tell me the best books from Springer Publisher you know that only require the prerequisites that I have, but that go deep.

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