|
A separable non-remainder of 
Author(s):
Alan
Dow;
Klaas Pieter
Hart
Journal:
Proc. Amer. Math. Soc.
136
(2008),
4057-4063.
MSC (2000):
Primary 54F15;
Secondary 03E50, 03E65, 54A35, 54D15, 54D40, 54D65
Posted:
May 27, 2008
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.
References:
- [1]
- J. M. Aarts and P. van Emde Boas, Continua as remainders in compact extensions, Nieuw Archief voor Wiskunde (3) 15 (1967), 34-37. MR 0214033 (35:4885)
- [2]
- A. V. Arhangelskiĭ, The power of bicompacta with first axiom of countability, Doklady Akademii Nauk SSSR 187 (1969), 967-970 (Russian); English transl., Soviet Mathematics Doklady 10 (1969), 951-955. MR 0251695 (40:4922)
- [3]
- Murray G. Bell, A first countable compact space that is not an
 image, Topology and its Applications 35 (1990), no. 2-3, 153-156. MR 1058795 (91m:54028) - [4]
- Eric K. van Douwen and Teodor C. Przymusiński, Separable extensions of first countable spaces, Fundamenta Mathematicae 105 (1979/80), no. 2, 147-158. MR 561588 (82j:54051)
- [5]
- Alan Dow and Klaas Pieter Hart,
 has (almost) no continuous images, Israel Journal of Mathematics 109 (1999), 29-39. MR 1679586 (2000d:54031) - [6]
- Alan Dow and Klaas Pieter Hart, The measure algebra does not always embed, Fundamenta Mathematicae 163 (2000), no. 2, 163-176. MR 1752102 (2001g:03089)
- [7]
- Alan Dow and Klaas Pieter Hart, A universal continuum of weight
 , Transactions of the American Mathematical Society 353 (2001), no. 5, 1819-1838. MR 1707489 (2001g:54037) - [8]
- Klaas Pieter Hart, The Čech-Stone compactification of the Real Line, Recent progress in general topology, 1992, pp. 317-352.
- [9]
- I. I. Parovičenko, On a universal bicompactum of weight
 , Soviet Mathematics Doklady 4 (1963), 592-595. Russian original: Ob odnom universal'nom bikompakte vesa  , Doklady Akademiı Nauk SSSR 150 (1963) 36-39. MR 27:719 - [10]
- Teodor C. Przymusiński, Perfectly normal compact spaces are continuous images of
 , Proceedings of the American Mathematical Society 86 (1982), no. 3, 541-544. MR 671232 (85c:54014) - [11]
- Stevo Todorčević, Partition problems in topology, Contemporary Mathematics, vol. 84, American Mathematical Society, Providence, RI, 1989. MR 980949 (90d:04001)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
54F15,
03E50, 03E65, 54A35, 54D15, 54D40, 54D65
Retrieve articles in all Journals with MSC
(2000):
54F15,
03E50, 03E65, 54A35, 54D15, 54D40, 54D65
Additional Information:
Alan
Dow
Affiliation:
Department of Mathematics, University of North Carolina, Charlotte, 9201 University City Blvd., Charlotte, North Carolina 28223-0001
Email:
adow@uncc.edu
Klaas Pieter
Hart
Affiliation:
Faculty of Electrical Engineering, Mathematics and Computer Science, TU Delft, Postbus 5031, 2600 GA Delft, The Netherlands
Email:
k.p.hart@tudelft.nl
DOI:
10.1090/S0002-9939-08-09357-X
PII:
S 0002-9939(08)09357-X
Keywords:
Separable continuum,
continuous image,
$\mathbb {H}^*$,
$\beta X$,
$\mathsf {OCA}$
Received by editor(s):
August 7, 2007,
Received by editor(s) in revised form:
September 19, 2007, and September 25, 2007
Posted:
May 27, 2008
Additional Notes:
The first author was supported by NSF grant DMS-0554896
Communicated by:
Julia Knight
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org