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)

 
 

 

On compactifications with path connected remainders


Author: Jan J. Dijkstra
Journal: Proc. Amer. Math. Soc. 136 (2008), 4461-4466
MSC (2000): Primary 54D40, 54D05
DOI: https://doi.org/10.1090/S0002-9939-08-09567-1
Published electronically: July 1, 2008
MathSciNet review: 2431063
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon.


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

  • 1. O. T. Alas, M. G. Tkačenko, V. V. Tkachuk, and R. G. Wilson, Connectifying some spaces, Topology Appl. 71 (1996), 203-215. MR 1397942 (98g:54039)
  • 2. P. L. Bowers, Dense embeddings of nowhere locally compact separable metric spaces, Topology Appl. 26 (1987), 1-12. MR 893799 (88g:54029)
  • 3. F. H. Croom, Principles of Topology, Saunders, Philadelphia, 1989.
  • 4. E. K. van Douwen, Remote Points, Dissertationes Math. 188 (1981), 1-45. MR 627526 (83i:54024)
  • 5. A. Emeryk and W. Kulpa, The Sorgenfrey line has no connected compactification, Comment. Math. Univ. Carolinae 18 (1977), 483-487. MR 0461437 (57:1422)
  • 6. R. Engelking, General Topology, PWN, Warsaw, 1975. MR 0500779 (58:18316a)
  • 7. G. Gruenhage, J. Kulesza, and A. Le Donne, Connectifications of metrizable spaces, Topology Appl. 82 (1998), 171-179. MR 1602455 (99a:54014)
  • 8. J. van Mill, The Infinite-Dimensional Topology of Function Spaces, North-Holland, Amsterdam, 2001. MR 1851014 (2002h:57031)
  • 9. J. R. Porter and R. G. Woods, Subspaces of connected spaces, Topology Appl. 68 (1996), 113-131. MR 1374077 (97a:54020)
  • 10. P. Simon, Two questions about connected compactifications, Topology Atlas (2003), http://at.yorku.ca/q/a/a/a/22.htm.
  • 11. S. Watson and R. G. Wilson, Embeddings in connected spaces, Houston J. Math. 19 (1993), 469-481. MR 1242433 (94k:54040)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54D40, 54D05

Retrieve articles in all journals with MSC (2000): 54D40, 54D05


Additional Information

Jan J. Dijkstra
Affiliation: Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Email: dijkstra@cs.vu.nl

DOI: https://doi.org/10.1090/S0002-9939-08-09567-1
Keywords: Separable metric space, compactification, remainder, path connected, locally path connected.
Received by editor(s): October 30, 2007
Published electronically: July 1, 2008
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society