We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a . In addition some nonperfect spaces with σ-disjoint bases are constructed.
@article{bwmeta1.element.bwnjournal-article-fmv143i3p221bwm, author = {Paul Szeptycki}, title = {Countably metacompact spaces in the constructible universe}, journal = {Fundamenta Mathematicae}, volume = {142}, year = {1993}, pages = {221-230}, zbl = {0794.54026}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv143i3p221bwm} }
Szeptycki, Paul. Countably metacompact spaces in the constructible universe. Fundamenta Mathematicae, Tome 142 (1993) pp. 221-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv143i3p221bwm/
[00000] [B] D. K. Burke, PMEA and first countable countably metacompact spaces, Proc. Amer. Math. Soc. 92 (1984), 455-460. | Zbl 0544.54017
[00001] [C] J. Chaber, Metacompactness and the class of MOBI, Fund. Math. 91 (1976), 211-217. | Zbl 0343.54010
[00002] [D] P. Davies, Nonperfect space with point-countable bases, Proc. Amer. Math. Soc. 77 (1979), 276-278. | Zbl 0412.54021
[00003] [vD] E. K. van Douwen, The integers and topology, in: K. Kunen and J. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 111-167.
[00004] [DTW] A. Dow, F. D. Tall and W. A. R. Weiss, New proofs of the consistency of the normal Moore space conjecture I, Topology Appl. 37 (1990), 33-51.
[00005] [F] W. G. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294-298. | Zbl 0314.54028
[00006] [FR] W. G. Fleissner and M. Reed, Paralindelöf spaces and spaces with a σ-locally countable base, Topology Proc. 2 (1977), 89-110. | Zbl 0402.54016
[00007] [K] K. Kunen, Set Theory, An Introduction to Independence Proofs, North-Holland, Amsterdam, 1980. | Zbl 0443.03021
[00008] [N1] P. Nyikos, A provisional solution to the normal Moore space problem, Proc. Amer. Math. Soc. 78 (1980), 429-435. | Zbl 0446.54030
[00009] [N2] P. Nyikos, Countably metacompact, locally countable spaces in the constructible universe, Topology Appl., to appear. | Zbl 0893.54017
[00010] [S] P. J. Szeptycki, Uncovering separation properties in the Easton model, preprint. | Zbl 0862.54019
[00011] [T1] F. D. Tall, Set-theoretic consistence results and topological theorems concerning the normal Moore space conjecture and related problems, Dissertationes Math. 148 (1977).
[00012] [T2] F. D. Tall, Covering and separation properties in the Easton model, Topology Appl. 28 (1988), 155-163.
[00013] [W] S. Watson, Separation in countably paracompact spaces, Trans. Amer. Math. Soc. 290 (1985), 831-842. | Zbl 0583.54013