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Van Douwen's problem on 0-dimensional images of ordered compacta
Author(s):
S.
Purisch
Journal:
Proc. Amer. Math. Soc.
126
(1998),
269-271.
MSC (1991):
Primary 54D70, 54F05;
Secondary 06A05, 54C05, 54D30, 54F50
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Abstract:
A compact 0-dimensional space has a  -separating rank 1 family of clopen sets iff it is the continuous image of a compact 0-dimensional linearly ordered space.
References:
- [B]
- A. E. Brouwer, A compact tree-like space is the continuous image of an ordered continuum, Report ZW 33, Math. Centre, Amsterdam, 1974.
- [C]
- J. L. Cornette, ``Image of a Hausdorff arc'' is cyclically extensible and reducible, Trans. Amer. Math. Soc. 199 (1974), 253-267. MR 51:11453
- [D]
- E. K. van Douwen, Problems Section, Top. Proc. 7 (1982), p. 384.
- [KM]
- S. Koppelberg and J. D. Monk, Pseudo-trees and Boolean algebras, Order 8 (1992), 359-374. MR 93i:06006
- [MW]
- J. van Mill and E. Wattel, Dendrons, in: H. R. Bennett and D. J. Lutzer (eds.), Topology and Order Structures Part I, Math. Centre Tract 142, Math. Centre, Amsterdam, 1981, pages 59-81. MR 82m:54037
- [Ni]
- J. Nikiel, Orderability properties of a zero-dimensional space which is the continuous image of an ordered compactum, Top. Appl. 31 (1989), 269-276. MR 90e:54076
- [Ny]
- P. J. Nyikos, personal communication.
- [P]
- S. Purisch, Problems Section, Top. Proc. 17 (1992), 412-413.
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Additional Information:
S.
Purisch
Affiliation:
Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124
Email:
purisch@cs.miami.edu
DOI:
10.1090/S0002-9939-98-04404-9
PII:
S 0002-9939(98)04404-9
Keywords:
0-dimensional,
continuous image,
linearly ordered compactum,
$T_0$-separating,
rank 1,
Boolean algebras,
dendron
Received by editor(s):
November 12, 1995
Communicated by:
James West
Copyright of article:
Copyright
1998,
American Mathematical Society
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