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Introduction

  • Ernest G. Manes
Part of the Graduate Texts in Mathematics book series (GTM, volume 26)

Abstract

“Groups,” “rings,” and “lattices” are definable in the language of finitary operations and equations. “Compact Hausdorff spaces” are also equationally definable except that the requisite operations (of ultrafilter convergence) are quite infinitary. On the other hand, systems of structured sets such as “topological spaces” cannot be presented using only operations and equations. While “topological groups” is not equational when viewed as a system of sets with structure, when viewed as a system of “topological spaces with structure” the additional structure is equational; here we must say equational “over topological spaces.”

Keywords

Topological Space Category Theory Additional Structure Algebraic Theory Compact Hausdorff 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

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • Ernest G. Manes
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA

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