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Elements of Topology

In: An Introduction to Nonlinear Analysis: Theory

Author

Listed:
  • Zdzisław Denkowski

    (Jagiellonian University, Faculty of Mathematics, Physics and Computer Science Institute of Computer Science)

  • Stanisław Migórski

    (Jagiellonian University, Faculty of Mathematics, Physics and Computer Science Institute of Computer Science)

  • Nikolas S. Papageorgiou

    (National Technical University, Department of Mathematics)

Abstract

In this chapter, we review the basic facts of general topology that will be used in this book. A detailed study of set-theoretic topology would be out of place here. Nevertheless, topology, continuity and convergence are integral parts in any study of nonlinear analysis having a serious claim to completeness. Topological notions play a central role in constructing the objects studied in Nonlinear Analysis and in carrying out proofs. Moreover, there are intimate connections between many basic fields of Nonlinear Analysis and topology. Measure theory, integration and differentiation, Banach space theory, degree theory, nonsmooth analysis, fixed point theory and critical point theory, to mention only a few, depend extensively on topological concepts and results. In asking the reader to go through the basic theory of point-set topology, with its high level of abstraction, we ask for a considerable preliminary effort. The reward will be a much more thorough presentation of contemporary Nonlinear Analysis.

Suggested Citation

  • Zdzisław Denkowski & Stanisław Migórski & Nikolas S. Papageorgiou, 2003. "Elements of Topology," Springer Books, in: An Introduction to Nonlinear Analysis: Theory, chapter 0, pages 1-102, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-9158-4_1
    DOI: 10.1007/978-1-4419-9158-4_1
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