Finitary substitute for continuous topology

  • Rafael D. Sorkin


Finite topological spaces are combinatorial structures that can serve as replacements for, or approximations to, bounded regions within continuous spaces such as manifolds. In this spirit, the present paper studies the approximation of general topological spaces by finite ones, or really by “finitary” ones in case the original space is unbounded. It describes how to associate a finitary spaceF with any locally finite covering of aT1-spaceS; and it shows howF converges toS as the sets of the covering become finer and more numerous. It also explains the equivalent description of finite topological spaces in order-theoretic language, and presents in this connection some examples of posetsF derived from simple spacesS. The finitary spaces considered here should not be confused with the so-called causal sets, but there may be a relation between the two notions in certain situations.


Manifold Field Theory Elementary Particle Quantum Field Theory Topological Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Rafael D. Sorkin
    • 1
  1. 1.Institute for Advanced StudyPrinceton

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