Title:
|
Centered-Lindelöfness versus star-Lindelöfness (English) |
Author:
|
Bonanzinga, M. |
Author:
|
Matveev, M. V. |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
41 |
Issue:
|
1 |
Year:
|
2000 |
Pages:
|
111-122 |
. |
Category:
|
math |
. |
Summary:
|
We discuss various generalizations of the class of Lindelöf spaces and study the difference between two of these generalizations, the classes of star-Lindelöf and centered-Lindelöf spaces. (English) |
Keyword:
|
star-Lindelöf |
Keyword:
|
centered-Lindelöf |
Keyword:
|
linked-Lindelöf |
Keyword:
|
CCC-Lindelöf |
Keyword:
|
metaLin- \linebreak delöf |
Keyword:
|
paraLindelöf |
Keyword:
|
weakly separable |
Keyword:
|
CCC |
Keyword:
|
$C_p(X)$ |
MSC:
|
54D20 |
MSC:
|
54G20 |
idZBL:
|
Zbl 1037.54502 |
idMR:
|
MR1756931 |
. |
Date available:
|
2009-01-08T18:59:01Z |
Last updated:
|
2012-04-30 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119145 |
. |
Reference:
|
[1] Arhangel'skii A.V.: Topological function spaces.Moskov. Gos. Univ. Publ., Moscow, 1989 (in Russian); English translation in: Mathematics and its Applications (Soviet Series) 78, Kluwer Academic Publishers Group, Dordrecht, 1992. MR 1144519 |
Reference:
|
[2] Arhangel'skii A.V.: $C_p$-theory.Recent Progress in General Topology, M. Hušek and J. van Mill Eds., Elsevier Sci. Pub. B.V., 1992, pp.1-56. Zbl 0932.54015 |
Reference:
|
[3] Arhangel'skii A.V., Ponomarev V.I.: Foundations of General Topology: Problems and Exercises.Moscow, Nauka Publ., 1974 (in Russian); English translation in: Mathematics and its applications, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster 13 (1984). MR 0785749 |
Reference:
|
[4] Asanov M.O.: On cardinal invariants of the spaces of all continuous functions (in Russian).Contemporary Topology and Set Theory, Izhevsk 2 (1979), 8-12. |
Reference:
|
[5] Berner A.J.: Spaces with dense conditionally compact subsets.Proc. Amer. Mat. Soc. 81 (1979), 137-142. MR 0589156 |
Reference:
|
[6] Beshimov R.B.: Weakly separable spaces and mappings.Thesis, Moscow State University, 1994. |
Reference:
|
[7] Beshimov R.B.: Some properties of weakly separable spaces Uzbek. Mat. Zh..1 (1994), 7-11. MR 1350283 |
Reference:
|
[8] Bonanzinga M.: Star-Lindelöf and absolutely star-Lindelöf spaces.Questions Answers Gen. Topology 16 (1998), 79-104. Zbl 0931.54019, MR 1642032 |
Reference:
|
[9] van Douwen E.K.: Density of compactifications.Set-Theoretic Topology, G.M. Reed Ed., N.Y., 1977, pp.97-110. Zbl 0379.54006, MR 0442887 |
Reference:
|
[10] van Douwen E.K.: The Pixley-Roy topology on spaces of subsets.Set-Theoretic Topology, G.M. Reed Ed., N.Y., 1977, pp.111-134. Zbl 0372.54006, MR 0440489 |
Reference:
|
[11] van Douwen E.K., Reed G.M., Roscoe A.W., Tree I.J.: Star covering properties.Topology Appl. 39 (1991), 71-103. Zbl 0743.54007, MR 1103993 |
Reference:
|
[12] Dow A., Junnila H., Pelant J.: Weak covering properties of weak topologies.Proc. London Math. Soc. (3) 75 (1997), 2 349-368. Zbl 0886.54014, MR 1455860 |
Reference:
|
[13] Engelking R.: General Topology.Warszawa, 1977. Zbl 0684.54001, MR 0500780 |
Reference:
|
[14] Fleischman W.M.: A new extension of countable compactness.Fund. Math. 67 (1970), 1-9. Zbl 0194.54601, MR 0264608 |
Reference:
|
[15] Ikenaga S.: A class which contains Lindelöf spaces, separable spaces and countably compact spaces.Mem. of Numazu College of Tech. 18 (1983), 105-108. |
Reference:
|
[16] Ikenaga S.: Topological concept between Lindelöf and Pseudo-Lindelöf.Res. Rep. of Nara Nat. College of Technology 26 (1990), 103-108. |
Reference:
|
[17] Levy R., McDowell R.H.: Dense subsets of $\beta X$.Proc. Amer. Mat. Soc. 507 (1975), 426-429. Zbl 0313.54025, MR 0370506 |
Reference:
|
[18] Matveev M.V.: Pseudocompact and related spaces.Thesis, Moscow State University, 1985. |
Reference:
|
[19] Matveev M.V.: A survey on star covering properties Topology Atlas, preprint No 330 (1998) http://www.unipissing.ca/topology/v/a/a/a/19.htm.. |
Reference:
|
[20] Matveev M.V., Uspenskii V.V.: On star-compact spaces with a $G_{\delta}$-diagonal.Zbornik Radova Filosofskogo Fakulteta v Nisu, Ser. Mat. 6:2 (1992), 281-290. Zbl 0911.54020, MR 1244780 |
Reference:
|
[21] Miller A.W.: Special subsets of the real line.Handbook of Set-Theoretic Topology, K. Kunen and J.E. Vaughan Eds., Elsevier Sci. Publ., 1984, pp.201-233. Zbl 0588.54035, MR 0776624 |
Reference:
|
[22] Pixley C., Roy P.: Uncompletable Moore spaces.Proceedings of the Auburn Topology Conference, Auburn Univ., Auburn, Alabama, 1969, pp.75-85. Zbl 0259.54022, MR 0397671 |
Reference:
|
[23] Pol R.: A theorem on weak topology on $C(X)$ for compact scattered $X$.Fund. Math. 106 2 (1980), 135-140. MR 0580591 |
Reference:
|
[24] Przymusiński T., Tall F.D.: The undecidability of the existence of a non-separable normal Moore space satisfying the countable chain condition.Fund. Math 85 (1974), 291-297. MR 0367934 |
Reference:
|
[25] Reznichenko E.A.: A pseudocompact space in which only the sets of full cardinality are not closed and not discrete.Vestnik MGU, Ser. I: Matem., Mekh., 1989, No. 6, pp.69-70 (in Russian); English translation in: Moscow Univ. Math. Bull. 44 (1989) 70-71. MR 1065983 |
Reference:
|
[26] Scott B.M.: Pseudocompact, metacompact spaces are compact.Topology Proc. 4 (1979), 577-587. MR 0598295 |
Reference:
|
[27] Tall F.D.: Normality versus collectionwise normality.Handbook of Set-Theoretic Topology, K. Kunen and J.E. Vaughan Eds., Elsevier Sci. Publ., 1984, pp.685-732. Zbl 0552.54011, MR 0776634 |
. |