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The Sorgenfrey line has a locally pathwise connected connectification
Author(s):
Alessandro
Fedeli;
Attilio
Le Donne
Journal:
Proc. Amer. Math. Soc.
129
(2001),
311-314.
MSC (2000):
Primary 54D35, 54D05
Posted:
July 27, 2000
MathSciNet review:
1694861
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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:
-
- 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:
10.1090/S0002-9939-00-05522-2
PII:
S 0002-9939(00)05522-2
Keywords:
Connected,
Sorgenfrey line
Received by editor(s):
July 24, 1997
Received by editor(s) in revised form:
March 25, 1999
Posted:
July 27, 2000
Communicated by:
Alan Dow
Copyright of article:
Copyright
2000,
American Mathematical Society
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