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).References
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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