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Fuzzy Reals: Topological Results Surveyed, Brouwer Fixed Point Theorem, Open Questions

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Topological and Algebraic Structures in Fuzzy Sets

Part of the book series: Trends in Logic ((TREN,volume 20))

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Abstract

There is no doubt that the L-reals ℝ (L) and, in particular, the unit L-interval I(L) are among the most important and canonical examples of L-topological spaces. These two spaces have a particularly well-established theory within the framework of the, so to say, classical fuzzy topology (as originated by Chang [1], Goguen [3], and Hutton [7, 8]). It is presently a part of so-called fixed-basis fuzzy topology (cf. Höhle [4] and Höhle and Šostak [5]) and even more a part of variable-basis fuzzy topology (cf. Rodabaugh [31] and Section 7 of [32]).

Partially supported by UPV: 127.310-EA018/99.

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Authors
  1. T. Kubiak
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Editors and Affiliations

  1. Department of Mathematics and Statistics, Youngstown State University, 44555-3609, Youngstown, Ohio, USA

    Stephen Ernest Rodabaugh

  2. Institut für Algebra, Stochastik und wissensbasierte mathematische Systeme, Johannes Kepler Universität, 4040, Linz, Austria

    Erich Peter Klement

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Kubiak, T. (2003). Fuzzy Reals: Topological Results Surveyed, Brouwer Fixed Point Theorem, Open Questions. In: Rodabaugh, S.E., Klement, E.P. (eds) Topological and Algebraic Structures in Fuzzy Sets. Trends in Logic, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0231-7_6

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  • DOI: https://doi.org/10.1007/978-94-017-0231-7_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6378-6

  • Online ISBN: 978-94-017-0231-7

  • eBook Packages: Springer Book Archive

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