Lindelöf property and absolute embeddings
Authors:
A. Bella and I. V. Yaschenko
Journal:
Proc. Amer. Math. Soc. 127 (1999), 907913
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 contains two disjoint closed copies and of , then these copies can be separated in by open sets. We also show that a Tychonoff space is weakly embedded (relatively normal) in every larger Tychonoff space if and only if 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
DOI:
http://dx.doi.org/10.1090/S0002993999045682
PII:
S 00029939(99)045682
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
