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

DOI:
https://doi.org/10.1090/S0002-9939-99-04568-2

MathSciNet review:
1469399

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-99-04568-2

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