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Rudin, M. E.

Hereditarily paracompact and compact monotonically normal spaces. (English) Zbl 0983.54021

Topology Appl. 111, No. 1-2, 179-189 (2001).
In [Quest. Answers Gen. Topology 4, 117-128 (1987; Zbl 0625.54039)] J. Nikiel has conjectured that every compact monotonically normal space is the continuous image of a compact linearly ordered space. In [Topology Appl. 82, No. 1-3, 397-419 (1998; Zbl 0889.54014); 85, No. 1-3, 319-333 (1998; Zbl 0983.54007), see above] the author has shown that every separable compact monotonically normal space is the continuous image of a compact linearly ordered space. In this paper she strengthens her partial solution of Nikiel’s conjecture by proving that every hereditarily paracompact compact monotonically normal space is the continuous image of a compact linearly ordered space. In the meantime she has settled the problem in its whole generality by proving that Nikiel’s conjecture is true (to appear).
Reviewer: H.Brandenburg (Berlin)

Cited in 3 Documents

MSC:

54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54B99 Basic constructions in general topology

Keywords:

countably tight space; hereditarily paracompact space; continuous image; compact linearly ordered space

Citations:

Zbl 0625.54039; Zbl 0889.54014; Zbl 0983.54007
PDFBibTeX XMLCite
\textit{M. E. Rudin}, Topology Appl. 111, No. 1--2, 179--189 (2001; Zbl 0983.54021)
Full Text: DOI

References:

[1] Balogh, Z.; Rudin, M. E., Monotone normality, Topology Appl., 47, 115-127 (1992) · Zbl 0769.54022
[2] Gartside, P. M., Cardinal invariants of monotonically normal spaces, Topology Appl., 77, 303-314 (1997) · Zbl 0872.54005
[3] Juhasz, I., Cardinal Functions in Topology, Math. Centre Tracts, 34 (1975), CWI: CWI Amsterdam, p. 115
[4] Nikiel, J., Some problems on continuous images of compact spaces, Questions Answers in Gen. Topology, 4, 117-128 (1986) · Zbl 0625.54039
[5] Rudin, M. E., Compact, separable, linearly ordered spaces, Topology Appl., 82, 397-419 (1998) · Zbl 0889.54014
[6] Rudin, M. E., Zero-dimensionality and monotone normality, Topology Appl., 85, 319-333 (1998) · Zbl 0983.54007
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