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Frederic Riesz’ Contributions to the Foundations of General Topology

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Handbook of the History of General Topology

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

Abstract

Frederic Riesz made significant suggestions as to how the axiomatic foundations of general topology might be formulated. These suggestions are contained in the two articles [1] and [2] which appeared, respectively, in 1906 and 1908. Unfortunately they were generally overlooked at that time and their importance was appreciated only after they were rediscovered much later. Even now (see [7] and [8]) they are not as well known as they deserve to be.

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References

  1. F. Riesz, Die Genesis des Raumbegriffs, Math. Naturwiss. Ber. Ungarn 24 (1906), 309–353.

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  2. F. Riesz, Stetigkeitsbegriff und abstrakte Mengenlehre, Atti IV Congr. Intern. Mat., Roma (1908) II, 18–24.

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  3. W. J. Thron, Topological Structures, Holt, Reinhart and Winston, New York, 1966.

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  4. W. J. Thron, On a problem of F. Riesz concerning proximity structures, Proc. Amer. Math. Soc. 40 (1973), 323–326.

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  5. W. J. Thron, Proximity Structures and Grills, Math. Ann. 206 (1973), 35–62.

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  6. W. J. Thron, What results are valid on closure spaces, Top. Proc. 6 (1981), 135–158.

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  7. R. L. Wilder, Evolution of the topological concept of “connected,” Amer. Math. Monthly 85 (1978), 720–726.

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  8. R. L. Wilder, Correction and Addendum to “Evolution of the topological concept of `connected’ ”, Amer. Math. Monthly 87 (1980), 31–32.

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Author information

Authors and Affiliations

  1. University of Colorado, Boulder, Colorado, USA

    W. J. Thron

Authors
  1. W. J. Thron
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Editor information

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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Thron, W.J. (1997). Frederic Riesz’ Contributions to the Foundations of General Topology. 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_2

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  • DOI: https://doi.org/10.1007/978-94-017-0468-7_2

  • 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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