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Israel Journal of Mathematics

, Volume 25, Issue 3–4, pp 249–272 | Cite as

Completeness theorems for continuous functions and product topologies

  • Joseph Sgro
Article

Abstract

In this paper we formulate a first order theory of continuous functions on product topologies via generalized quantifiers. We present an axiom system for continuous functions on product topologies and prove a completeness theorem for them with respect to topological models. We also show that if a theory has a topological model which satisfies the Hausdorff separation axiom, then it has a 0-dimensional, normal topological model. We conclude by obtaining an axiomatization for topological algebraic structures, e.g. topological groups, proving a completeness theorem for the analogue with countable conjunctions and disjunctions, and presenting counterexamples to interpolation and definability.

Keywords

Topological Space Topological Group Topological Model Product Topology Completeness Theorem 
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

© Hebrew University 1976

Authors and Affiliations

  • Joseph Sgro
    • 1
    • 2
  1. 1.University of WisconsinUSA
  2. 2.Yale UniversityYaleUSA

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