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Lindelöf property and absolute embeddings

Authors: A. Bella and I. V. Yaschenko
Journal: Proc. Amer. Math. Soc. 127 (1999), 907-913
MSC (1991): Primary 54A35, 54D20
MathSciNet review: 1469399
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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

I. V. Yaschenko
Affiliation: Moscow Center for Continuous Mathematical Education, B.Vlas’evskij per. 11, 121002, Moscow, Russia

Keywords: Lindel\"{o}f space, normal space, relative topological property, embedding, almost compact space
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
Article copyright: © Copyright 1999 American Mathematical Society