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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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The orderability and closed images of scattered spaces
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by S. Purisch PDF
Trans. Amer. Math. Soc. 320 (1990), 713-725 Request permission

Abstract:

A (totally) orderable scattered space and a space homeomorphic to a subspace of an ordinal space are characterized in terms of a neighborhood subbase for each of their points plus what corresponds to a neighborhood base for each of their non-$Q$-gaps. These generalize the characterizations in [ P$_{1}$] of an orderable compact scattered space and in [B] of a space homeomorphic to a compact ordinal space. Generalizing a result in [M] it is shown that a space is orderable and scattered iff it is the $2$ to $1$ image under a closed map of a subspace of an ordinal space. In response to a question of Telgarsky [T] a simple description is given of a closed map with discrete fibers from an orderable scattered space onto an orderable perfect space. Maps that preserve length conditions on a scattered space are touched upon.
References
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 320 (1990), 713-725
  • MSC: Primary 54F05; Secondary 54D99
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0989584-0
  • MathSciNet review: 989584