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Interaction between General Topology and Functional Analysis

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Handbook of the History of General Topology

Part of the book series: History of Topology ((HIPO,volume 1))

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Abstract

This paper concerns the history of the interaction between topology and analysis. As a theory, topology began in 1847 (Sec. 1, Listing). The first phase (1847–1887) was a development of topology under the influence of classical analysis, in particular, complex analysis (Sec. 2, Riemann) and the calculus of variations (Sec. 3, Weierstrass). General set theory was born in 1874 (Sec. 2, Cantor). This was the necessary starting point of set-theoretic topology (also called general topology), which plays a greater role in analysis than combinatorial topology (initiated by Poincaré) and algebraic topology do (Sec. 5).

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Authors and Affiliations

  1. Carleton University, Ottawa, Canada

    Erwin Kreyszig

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  1. Erwin Kreyszig
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Editors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

    C. E. Aull

  2. Department of Mathematics and Computer Science, University of Antwerp, RUCA, Antwerp, Belgium

    R. Lowen

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© 1997 Springer Science+Business Media Dordrecht

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Kreyszig, E. (1997). Interaction between General Topology and Functional Analysis. In: Aull, C.E., Lowen, R. (eds) Handbook of the History of General Topology. History of Topology, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0468-7_17

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  • DOI: https://doi.org/10.1007/978-94-017-0468-7_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4820-2

  • Online ISBN: 978-94-017-0468-7

  • eBook Packages: Springer Book Archive

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