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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lindelöf property and absolute embeddings
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by A. Bella and I. V. Yaschenko PDF
Proc. Amer. Math. Soc. 127 (1999), 907-913 Request permission


It is proved that a Tychonoff space is Lindelöf if and only if whenever a Tychonoff space $Y$ contains two disjoint closed copies $X_{1}$ and $X_{2}$ of $X$, then these copies can be separated in $Y$ by open sets. We also show that a Tychonoff space $X$ is weakly $C$-embedded (relatively normal) in every larger Tychonoff space if and only if $X$ is either almost compact or Lindelöf (normal almost compact or Lindelöf).
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Additional Information
  • A. Bella
  • Affiliation: Dipartimento di Matematica, Citta Universitaria, Viale A.Doria 6, 95125, Catania, Italy
  • Email:
  • I. V. Yaschenko
  • Affiliation: Moscow Center for Continuous Mathematical Education, B.Vlas’evskij per. 11, 121002, Moscow, Russia
  • Email:
  • Received by editor(s): November 14, 1996
  • Received by editor(s) in revised form: June 26, 1997
  • Additional Notes: This work was done while the second author was visiting Catania University. He is grateful to Italian colleagues for generous hospitality and to CNR for financial support.
  • Communicated by: Alan Dow
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 907-913
  • MSC (1991): Primary 54A35, 54D20
  • DOI:
  • MathSciNet review: 1469399