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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Set convergences. An attempt of classification
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by Yves Sonntag and Constantin Zălinescu PDF
Trans. Amer. Math. Soc. 340 (1993), 199-226 Request permission

Abstract:

We endow families of nonempty closed subsets of a metric space with uniformities defined by semimetrics. Such structure is completely determined by a class (which is a family of closed sets) and a type (which is a semimetric). Two types are sufficient to define (and classify) almost all convergences known till now. These two types offer the possibility of defining other set convergences.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 340 (1993), 199-226
  • MSC: Primary 54A20; Secondary 54B20, 54D55, 54E15
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1173857-8
  • MathSciNet review: 1173857