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Proceedings of the American Mathematical Society

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

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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

Abstract:

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: bella@dipmat.unict.it
  • I. V. Yaschenko
  • Affiliation: Moscow Center for Continuous Mathematical Education, B.Vlas’evskij per. 11, 121002, Moscow, Russia
  • Email: ivan@mccme.ru
  • 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: https://doi.org/10.1090/S0002-9939-99-04568-2
  • MathSciNet review: 1469399