Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [Ar] A. V. Arhangel′skii, Relative topological properties and relative topological spaces, Proceedings of the International Conference on Convergence Theory (Dijon, 1994), 1996, pp. 87–99. MR 1397067,
  • [AG] A.V.Arhangel'skij and H.M.M.Genedi, Beginnings of the theory of relative topological properties, General Topology, Spaces and Mappings, MGU, Moscow, 1989, pp. 87-89.
  • [AT] A. V. Arhangel′skii and J. Tartir, A characterization of compactness by a relative separation property, Questions Answers Gen. Topology 14 (1996), no. 1, 49–52. MR 1384052
  • [BH] Robert L. Blair and Anthony W. Hager, Extensions of zero-sets and of real-valued functions, Math. Z. 136 (1974), 41–52. MR 385793,
  • [Bl] Robert L. Blair, On 𝜐-embedded sets in topological spaces, TOPO 72—general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. de Groot), Springer, Berlin, 1974., pp. 46–79. Lecture Notes in Math., Vol. 378. MR 0358677
  • [HJ] Anthony W. Hager and Donald G. Johnson, A note on certain subalgebras of 𝐶(𝔛), Canadian J. Math. 20 (1968), 389–393. MR 222647,
  • [En] Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna. Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
  • [GJ] Leonard Gillman and Meyer Jerison, Rings of continuous functions, Springer-Verlag, New York-Heidelberg, 1976. Reprint of the 1960 edition; Graduate Texts in Mathematics, No. 43. MR 0407579
  • [He] E.Hewitt, A note on extensions of continuous functions, An. Acad. Brasil. Ci. 21 (1949), 175-179. MR 11:194c
  • [Ku] K. Kunen, Combinatorics, Handbook of Mathematical Logic (J. Barwise, eds.), Elsevier S.P., North-Holland, Amsterdam, 1977.
  • [Sm] Yu.Smirnov, Mappings of systems of open sets (in Russian), Matem. Sbornik 31 (1952), 152-166. MR 14:303g
  • [St] R. M. Stephenson Jr., Initially 𝜅-compact and related spaces, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 603–632. MR 776632
  • [Wa] S. Watson, The Construction of Topological Spaces: Planks and Resolutions, Recent Progress in General Topology (M. Husek and J. van Mill, eds.), Elsevier S.P., North-Holland, Amsterdam, 1992, pp. 673-757. CMP 93:15

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54A35, 54D20

Retrieve articles in all journals with MSC (1991): 54A35, 54D20

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