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The Sorgenfrey line has a locally pathwise connected connectification


Authors: Alessandro Fedeli and Attilio Le Donne
Journal: Proc. Amer. Math. Soc. 129 (2001), 311-314
MSC (2000): Primary 54D35, 54D05
DOI: https://doi.org/10.1090/S0002-9939-00-05522-2
Published electronically: July 27, 2000
MathSciNet review: 1694861
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Abstract | References | Similar Articles | Additional Information

Abstract: We answer a question of Alas, Tkacenko, Tkachuk and Wilson by constructing a connected locally pathwise connected Hausdorff space in which the Sorgenfrey line can be densely embedded.


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

  • 1. O.T. Alas, M.G. Tkacenko, V.V. Tkachuk and R.G. Wilson, Connectedness and local connectedness of topological groups and extensions, preprint.
  • 2. A. Emeryk and W. Kulpa, The Sorgenfrey line has no connected compactification, Comm. Math. Univ. Carolinae 18 (1977), 483-487. MR 57:1422
  • 3. R. Engelking, General Topology, Sigma series in Pure Mathematics 6, Heldermann Verlag, Berlin, 1989. MR 91c:54001
  • 4. A. Fedeli and A. Le Donne, Dense embeddings in pathwise connected spaces, Topology and its Applications 96 (1999), 15-22. CMP 99:16
  • 5. J. Porter and J. Vermeer, Spaces with coarser minimal Hausdorff topologies, Trans. Amer. Math. Soc. 289 (1985), 59-71. MR 86h:54030
  • 6. S. Watson and S. Wilson, Embeddings in connected spaces, Houston J. Math. 19 (1993), no. 3, 469-481. MR 94k:54040

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Additional Information

Alessandro Fedeli
Affiliation: Department of Mathematics, University of L’Aquila, 67100 L’Aquila, Italy
Email: alessandro.fedeli@axscaq.aquila.infn.it

Attilio Le Donne
Affiliation: Department of Mathematics, University of Rome “La Sapienza", 00100 Rome, Italy
Email: ledonne@mat.uniroma1.it

DOI: https://doi.org/10.1090/S0002-9939-00-05522-2
Keywords: Connected, Sorgenfrey line
Received by editor(s): July 24, 1997
Received by editor(s) in revised form: March 25, 1999
Published electronically: July 27, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society

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