| Title:
|
Order-like structure of monotonically normal spaces (English) |
| Author:
|
Williams, Scott W. |
| Author:
|
Zhou, Haoxuan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
207-217 |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a compact monotonically normal space X we prove: \, (1) \, $X$ has a dense set of points with a well-ordered neighborhood base (and so $X$ is co-absolute with a compact orderable space); \, (2) \, each point of $X$ has a well-ordered neighborhood $\pi $-base (answering a question of Arhangel'skii); \, (3) \, $X$ is hereditarily paracompact iff $X$ has countable tightness. In the process we introduce weak-tightness, a notion key to the results above and yielding some cardinal function results on monotonically normal spaces. (English) |
| Keyword:
|
monotonically normal |
| Keyword:
|
compactness |
| Keyword:
|
linear ordered spaces |
| MSC:
|
54D15 |
| MSC:
|
54D30 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 0937.54012 |
| idMR:
|
MR1623026 |
| . |
| Date available:
|
2009-01-08T18:40:07Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118999 |
| . |
| Reference:
|
[Ar1] Arhangel'skii A.V.: Structure and classification of topological spaces and cardinal invariants.Russian Math. Surv. 33 (1977), 33-95. MR 0526012 |
| Reference:
|
[Ar2] Arhangel'skii A.V.: Some properties of radial spaces.Math. Zametki 27 (1980), 95-104. MR 0562480 |
| Reference:
|
[BR] Balogh Z., Rudin M.E.: Monotone Normality.Topology and Appl. 47 (1992), 115-127. Zbl 0769.54022, MR 1193194 |
| Reference:
|
[Bo1] Borges C.J.R.: On stratifiable spaces.Pacific J. Math. 17 (1966), 1-16. Zbl 0175.19802, MR 0188982 |
| Reference:
|
[Bo2] Borges C.J.R.: Direct sums of stratifiable spaces.Fundamenta Math. 100 (1978), 95-99. Zbl 0389.54018, MR 0505891 |
| Reference:
|
[En] Engelking R.: General Topology.Polish Scientific Publishers, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[Gr] Gruenhage G.: Generalized metric spaces.Handbook of Set-theoretic Topology, North Holland, 1984, pp.423-502. Zbl 0794.54034, MR 0776629 |
| Reference:
|
[HLZ] Heath R.W., Lutzer D.J., Zenor P.L.: Monotonically normal spaces.Trans. Amer. Math. Soc. 155 (1973), 481-494. Zbl 0269.54009, MR 0372826 |
| Reference:
|
[Ho] Hodel R.: Cardinal Functions I.Handbook of set-theoretic Topology, North Holland, 1984, pp.1-61. Zbl 0559.54003, MR 0776620 |
| Reference:
|
[Ju] Juhasz I.: Cardinal Functions in Topology.Math. Centre Tracts 34, 1971. Zbl 0479.54001, MR 0340021 |
| Reference:
|
[Ni] Nikiel J.: Some problems on continuous images of compact ordered spaces.Quest. & And. in Gen. Top. 4 (1986), 117-128. MR 0917893 |
| Reference:
|
[NP] Nyikos P.J., Purisch S.: Monotone normality and paracompactness in scattered spaces.Annals on the New York Acad. Sci. 552, 1989, pp.124-137. Zbl 0887.54019, MR 1020780 |
| Reference:
|
[Os] Ostacewski A.: Monotone normality and $G_\delta $-diagonals in the class of inductively generated spaces.Coll. Math. Soc. Janos Bolyai, Topology 23 (1978), 905-930. MR 0588837 |
| Reference:
|
[Ru1] Rudin M.E.: Dowker spaces.Handbook of Set-theoretic Topology, North Holland, 1984, pp.761-780. Zbl 0566.54009, MR 0776636 |
| Reference:
|
[Ru2] Rudin M.E.: Monotone normality and compactness.to appear in Topology and Appl. volume of Ehime Conference Proceedings, 1995. Zbl 0874.54004, MR 1425938 |
| Reference:
|
[Ru3] Rudin M.E.: Compact monotonically normal spaces.invited lecture, 8th Prague Topological Symposium, August, 1996. Zbl 0983.54021 |
| Reference:
|
[St] Stephenson R.M., Jr.: Initially $k$-compact and related spaces.Handbook of Set-theoretic Topology, North Holland, 1984, pp.603-602. MR 0776632 |
| Reference:
|
[UH] HASH(0x976e968): The University of Houston Problem Book, 6/30/90.. |
| Reference:
|
[Wi] Williams S.W.: Trees, Gleason spaces, and co-absolutes of $\beta N$-$N$.Trans. Amer. Math. Soc. 271 (1982), 83-100. MR 0648079 |
| Reference:
|
[WZ] Williams S.W., Zhou H.: Strong versions of normality.Proceedings of the New York Conference on Topology and its Applications. Zbl 0797.54011 |
| . |
