Strong paracompactness and w-$\delta \theta$-refinability of inverse limits
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Abstract:
In this paper we construct inverse systems of which each space is strongly paracompact and each bonding map and each projection are open and onto maps, and the limit space is paracompact and not strongly paracompact and we investigate $\delta \theta$-refinability-like properties of limit spaces of inverse systems.References
- Yasushi Aoki, Orthocompactness of inverse limits and products, Tsukuba J. Math. 4 (1980), no. 2, 241–255. MR 623438, DOI 10.21099/tkbjm/1496159177
- Keiko Chiba, Normality of inverse limits, Math. Japon. 35 (1990), no. 5, 959–970. MR 1073898
- Keiko Chiba, The strong paracompactness of $\sigma$-products, Sci. Math. 2 (1999), no. 3, 285–292. MR 1718269
- Keiko Chiba, Covering properties of inverse limits, Questions Answers Gen. Topology 20 (2002), no. 2, 101–114. MR 1931482
- Keiko Chiba, Expandabilities and covering properties of inverse limits, Rep. Fac. Sci. Shizuoka Univ. 37 (2003), 1–19 (English, with English and Japanese summaries). MR 1987955
- Keiko Chiba and Yukinobu Yajima, Covering properties of inverse limits. II, Proceedings of the Spring Topology and Dynamical Systems Conference, 2003, pp. 79–100. MR 2048923
- R. Engelking, General Topology, Polish Scientific publishers, Warszawa (1988).
- Heikki J. K. Junnila, On submetacompactness, Topology Proc. 3 (1978), no. 2, 375–405 (1979). MR 540503
- John Mack, Directed covers and paracompact spaces, Canadian J. Math. 19 (1967), 649–654. MR 211382, DOI 10.4153/CJM-1967-059-0
- Keiô Nagami, A note on Hausdorff spaces with the star-finite property. I, II, Proc. Japan Acad. 37 (1961), 131–134, 189–192. MR 144306
- Keiô Nagami, Countable paracompactness of inverse limits and products, Fund. Math. 73 (1971/72), no. 3, 261–270. MR 301688, DOI 10.4064/fm-73-3-261-270
- A. H. Stone, Inverse limits of compact spaces, General Topology Appl. 10 (1979), no. 2, 203–211. MR 527845, DOI 10.1016/0016-660x(79)90008-4
- J. M. W. Worrell, Some properties of full normality and their relations to Cech completeness, Notices Amer. Math. Soc., vol. 14 (1967), 555.
- Yoshikazu Yasui, Generalized paracompactness, Topics in general topology, North-Holland Math. Library, vol. 41, North-Holland, Amsterdam, 1989, pp. 161–202. MR 1053196, DOI 10.1016/S0924-6509(08)70151-X
Additional Information
- Keiko Chiba
- Affiliation: Department of Mathematics, Faculty of Science, Shizuoka University, Ohya, Surugaku, Shizuoka, 422-8529 Japan
- Email: smktiba@ipc.shizuoka.ac.jp
- Received by editor(s): June 10, 2003
- Received by editor(s) in revised form: November 2, 2004
- Published electronically: August 29, 2005
- Communicated by: Alan Dow
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1213-1221
- MSC (2000): Primary 54B10, 54D20; Secondary 54G20
- DOI: https://doi.org/10.1090/S0002-9939-05-08042-1
- MathSciNet review: 2196059