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Manifolds: Hausdorffness versus homogeneity


Authors: Mathieu Baillif and Alexandre Gabard
Journal: Proc. Amer. Math. Soc. 136 (2008), 1105-1111
MSC (2000): Primary 57N99, 54D10, 54E52.
DOI: https://doi.org/10.1090/S0002-9939-07-09100-9
Published electronically: November 30, 2007
MathSciNet review: 2361887
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Abstract: We analyze the relationship between Hausdorffness and homogeneity in the frame of manifolds not confined to be Hausdorff. We exhibit examples of homogeneous non-Hausdorff manifolds and prove that a Lindelöf homogeneous manifold is Hausdorff.


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

  • 1. N. Bourbaki.
    Elements of Mathematics: General Topology, Chapters 1-4, Chapters 5-10 (2nd printing).
    Springer-Verlag, Berlin, 1989. MR 979294 (90a:54001a)
  • 2. D.B. Fuks and V.A. Rokhlin.
    Beginner's Course in Topology.
    Springer-Verlag, Berlin, 1984. MR 759162 (86a:57001)
  • 3. D. Gauld.
    Strong contractibility.
    Indian J. Math. 25(1) (1983), 29-32. MR 809703 (86k:55005)
  • 4. A. Haefliger and G. Reeb.
    Variétés (non séparées) à une dimension et structures feuilletées du plan.
    Enseignement Math. (2) 3 (1957), 107-125. MR 0089412 (19:671c)
  • 5. P. Nyikos.
    The theory of nonmetrizable manifolds.
    In Handbook of Set-Theoretic Topology, 633-684, North-Holland, Amsterdam, 1984. MR 776633 (86f:54054)
  • 6. M.E. Rudin and P. Zenor.
    A perfectly normal nonmetrizable manifold.
    Houston J. Math. 2(1) (1976), 129-134. MR 0394560 (52:15361)
  • 7. M. Spivak.
    Differential Geometry, Vol. 1.
    Publish or Perish, New York, 1970.
  • 8. Z. Szentmiklóssy.
    S-spaces and L-spaces under Martin's axiom.
    In Á Császár, ed., Topology, Vol. II, Colloq. Math. Soc. J. Bolyai 23, 1139-1145, North-Holland, Amsterdam, 1980. MR 588860 (81k:54032)
  • 9. D. van Dantzig.
    Ueber topologisch homogene Kontinua.
    Fund. Math. 15 (1930), 102-125.
  • 10. W. Vick.
    Homology Theory: An Introduction to Algebraic Topology (2nd ed.).
    Graduate texts in mathematics, Springer-Verlag, Berlin, 1994. MR 1254439 (94i:55002)

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Additional Information

Mathieu Baillif
Affiliation: Université de Genève, Section de Mathématiques, 2-4, rue du Lièvre, CP 64, 1211 Genève 4, Suisse
Email: baillif@math.unige.ch

Alexandre Gabard
Affiliation: Université de Genève, Section de Mathématiques, 2-4, rue du Lièvre, CP 64, 1211 Genève 4, Suisse
Email: alexandregabard@hotmail.com

DOI: https://doi.org/10.1090/S0002-9939-07-09100-9
Received by editor(s): September 5, 2006
Received by editor(s) in revised form: November 1, 2006
Published electronically: November 30, 2007
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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