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      Natural Topology

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          Abstract

          We give a theoretical and applicable framework for dealing with real-world phenomena. Joining pointwise and pointfree notions in BISH, natural topology gives a faithful idea of important concepts and results in intuitionism. Natural topology is well-suited for practical and computational purposes. We give several examples relevant for applied mathematics, such as the decision-support system Hawk-Eye (used in professional tennis), and various real-number representations. We compare CLASS, INT, RUSS, BISH and formal topology. There are links with physics, regarding the topological character of our physical universe. Translation of intuitionistic results to BISH is facilitated by our framework, using transfinite countable-ordinal induction in Brouwer's style. We study quotients of Baire space, and obtain constructive metrizability of star-finitary spaces. Silva spaces arise as example of non-metrizable natural spaces. Finally we discuss the role of Church's Thesis in physics.

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          Author and article information

          Journal
          23 October 2012
          Article
          1210.6288
          3a15ef33-924a-48bb-b9c6-e19f7e5f61aa

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          03F65 (Primary) 54E99 03B30 03F55 03-02 54-02 (Secondary)
          174 pages, 1 illustration
          math.LO

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