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Overview

In: Continuity Theory

Author

Listed:
  • Louis Nel

    (Carleton University, School of Mathematics and Statistics)

Abstract

Continuity theory serves as infrastructure for more specialized mathematical theories such as ordinary differential equations, partial differential equations, integral equations, operator theory, dynamical systems, and global analysis. The infrastructure includes creation of new spaces out of given ones, extension theorems, existence theorems, inversion theorems, approximation theorems, factorization theorems, adjunctions (e.g., exponential laws), and (local) representation theorems. So it embodies a great variety of possible topics. The present book, while deliberately not encyclopedic, does include a systematic study of linear continuity—enough to provide a foundation for functional analysis (the linear part of continuity theory).

Suggested Citation

  • Louis Nel, 2016. "Overview," Springer Books, in: Continuity Theory, chapter 0, pages 1-16, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31159-3_1
    DOI: 10.1007/978-3-319-31159-3_1
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