Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
star-Lindelöf; centered-Lindelöf; linked-Lindelöf; CCC-Lindelöf; metaLin- \linebreak delöf; paraLindelöf; weakly separable; CCC; $C_p(X)$
star-Lindelöf; centered-Lindelöf; linked-Lindelöf; CCC-Lindelöf; metaLin- \linebreak delöf; paraLindelöf; weakly separable; CCC; $C_p(X)$
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.
References:
[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
[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
[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
[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.
[5] Berner A.J.: Spaces with dense conditionally compact subsets. Proc. Amer. Mat. Soc. 81 (1979), 137-142. MR 0589156
[6] Beshimov R.B.: Weakly separable spaces and mappings. Thesis, Moscow State University, 1994.
[7] Beshimov R.B.: Some properties of weakly separable spaces Uzbek. Mat. Zh. 1 (1994), 7-11. MR 1350283
[8] Bonanzinga M.: Star-Lindelöf and absolutely star-Lindelöf spaces. Questions Answers Gen. Topology 16 (1998), 79-104. MR 1642032 | Zbl 0931.54019
[9] van Douwen E.K.: Density of compactifications. Set-Theoretic Topology, G.M. Reed Ed., N.Y., 1977, pp.97-110. MR 0442887 | Zbl 0379.54006
[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. MR 0440489 | Zbl 0372.54006
[11] van Douwen E.K., Reed G.M., Roscoe A.W., Tree I.J.: Star covering properties. Topology Appl. 39 (1991), 71-103. MR 1103993 | Zbl 0743.54007
[12] Dow A., Junnila H., Pelant J.: Weak covering properties of weak topologies. Proc. London Math. Soc. (3) 75 (1997), 2 349-368. MR 1455860 | Zbl 0886.54014
[13] Engelking R.: General Topology. Warszawa, 1977. MR 0500780 | Zbl 0684.54001
[14] Fleischman W.M.: A new extension of countable compactness. Fund. Math. 67 (1970), 1-9. MR 0264608 | Zbl 0194.54601
[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.
[16] Ikenaga S.: Topological concept between Lindelöf and Pseudo-Lindelöf. Res. Rep. of Nara Nat. College of Technology 26 (1990), 103-108.
[17] Levy R., McDowell R.H.: Dense subsets of $\beta X$. Proc. Amer. Mat. Soc. 507 (1975), 426-429. MR 0370506 | Zbl 0313.54025
[18] Matveev M.V.: Pseudocompact and related spaces. Thesis, Moscow State University, 1985.
[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</b>
[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. MR 1244780 | Zbl 0911.54020
[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. MR 0776624 | Zbl 0588.54035
[22] Pixley C., Roy P.: Uncompletable Moore spaces. Proceedings of the Auburn Topology Conference, Auburn Univ., Auburn, Alabama, 1969, pp.75-85. MR 0397671 | Zbl 0259.54022
[23] Pol R.: A theorem on weak topology on $C(X)$ for compact scattered $X$. Fund. Math. 106 2 (1980), 135-140. MR 0580591
[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
[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
[26] Scott B.M.: Pseudocompact, metacompact spaces are compact. Topology Proc. 4 (1979), 577-587. MR 0598295
[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. MR 0776634 | Zbl 0552.54011
Search
Partner of
