Gerlits and function spaces

Studia Scientiarum Mathematicarum Hungarica

Volumn 47, Issue 4, 2010, Pages 529-557

  Scheepers, Marion ^a  

^a BOISE STATE UNIVERSITY   (United States)

Author keywords

03E05; 03E17; 03E35; 03E75; 05C55; 54A20; 54C35; 54D20; 54E99; 54G99; 91A44; Borel conjecture; Frech t Urysohn property; function space; game theory; gamma space; Gerlits Nagy space; Hurewicz space; ramsey theory; Rothberger space; tightness

Indexed keywords

EID: 78650775232     PISSN: 00816906     EISSN: 15882896     Source Type: Journal    
DOI: 10.1556/SScMath.47.2010.4.1161     Document Type: Article

References (53)

1. Arkhangelskii, A. V., Topological function spaces, Kluwer Academic Publishers 1992. MR 1144519 92i:54022
2. Babinkostova, L., Metrizable groups and strict o-boundedness, Mathematichki Vesnik, 58 (2006), 131-138. MR 2318228 2008b:54055
3. Babinkostova, L., On some questions about selective separability, Mathematical Logic Quarterly, 555 (2009), 539-541. MR 2568764 2010i:54026
4. Babinkostova, L., Guido, C. and Kocinac, Lj. D. R., On relative gamma sets, East-West Journal of Mathematics, 2 (2000), 195-199. MR 1825456 2001m:54016
5. Babinkostova, L. and Scheepers, M., Products and selection principles, Topology Proceedings, 31 (2007), 431-443. MR 2476622 2010b:54015
6. N, Topology and its Applications, 157 (2010), no. 8, 1302-1313. MR 2610440
7. Bartoszynski, T. and Reclaw, I., Not every ?-set is strongly meager, Contemporary Mathematics, 192 (1996), 25-29. MR 1367132 96k:03110
8. Bartoszynski, T. and Shelah, S., Continuous images of sets of reals, Topology and its Applications, 116 (2001), 243-253.
9. Bartoszynski, T. and Tsaban, B., Hereditary topological diagonalizations and the Menger-Hurewicz conjectures, Proceedings of the American Mathematical Society, 134 (2005), no. 2, 605-615.
10. Berner A. and Juhász, I., Point picking games and HFD's, in: Models and Sets, Proceedings of the Logic Colloquium 1983, Springer-Verlag Lecture Notes in Mathematics, 1103 (1984), 53-66. MR 0775687 86c:54005
11. Bella, A., Bonanzinga, M. and Matveev, M., Variations of selective separability, Topology and its Applications, 1567 (2009), 1241-1252. MR 2505000 2010d:54038
12. Bella, A., Bonanzinga, M., Matveev, M. and Tkachuk, V. V., Selective separability: General facts and behavior in counable spaces, Topology Proceedings, 32 (2008), 15-32. MR 1500068 2010a:54007
13. Blass, Andreas, Combinatorial Cardinal Characteristics of the Continuum, to appear as a chapter in Handbook of Set Theory (ed. M. Foreman, M. Magidor and A. Kanamori). A preprint is available at http://www.math.lsa.umich.edu/~ablass/ set.html
14. Carlson, T. J., Strong measure zero and strongly meager sets, Proceedings of the American Mathematical Society, 1182 (1993), 577-586. MR 1139474 94b:03086
15. Comfort, W. W. and Ross, K. A., Pseudocompactness and uniform continuity in topological groups, Pacific Journal of Mathematics, 163 (1966), 483-496. MR 0207886 34#7699
16. Fremlin, D. H. and Miller, A. W., On some properties of Hurewicz, Menger and Rothberger, Fundamenta Mathematicae, 129 (1988), 17-33. MR 0954892 89g:54061
17. Galvin, F., Indeterminacy of point-open games, Bull. Acad. Polon. Sci., 26 (1978), 445-449. MR 0493925 58#12881
18. Galvin, F. and Miller, A. W. On ?-sets and other singular sets of real numbers, Topology and its Applications, 17 (1984), 145-155. MR 0738943 85f:54011
19. Gerlits, J. and Nagy, Zs., Some properties of C(X), I, Topology and its Applications, 142 (1982), 151-161. MR 0667661 84f:54021
20. Gerlits, J., Some properties of C(X), II, Topology and its Applications, 15 (1983), 255-262. MR 0694545 84i:54018
21. d, Proceedings of the American Mathematical Society, 118 (1993), 603-607. MR 1132417 93g:03046
22. Gruenhage, G., Infinite games and generalizations of first countable spaces, General Topology and its Applications, 6 (1976), no. 3, 339-352. MR 0413049 54#1170
23. Gruenhage, G. and Ma, D. K., Baireness of Ck(X) for locally compact X, Topology and its Applications, 80 (1997), 131-139. MR 1469473 98f:54018
24. Jordan, F., There are no hereditary productive ?-spaces, Topology and its Applications, 155 (2008), no. 16, 1786-1791. MR 2445301 2009f:54029
25. Laver, R., On the consistency of Borel' Conjecture, Acta Mathematica, 1371 (1976), no. 3-4, 151-169. MR 0422027 54#10019
26. Di Maio, G., Kocinac, Lj. D. R. and Meccariello, E., Selection principles and hyperspace topologies, Topology and its Applications153 (2005), 912-923. MR 2203900 2006j:54011
27. Kocinac, Lj. D. R. and Scheepers, M., Function spaces and a property of Reznichenko, Topology and its Applications, 123 (2002), 135-143. MR 1921655 2003g:54036
28. Kocinac, Lj. D. R. and Scheepers, M., Combinatorics of open covers (VII): Groupability, Fundamenta Mathematicae, 179 (2003), 131-155. MR 2029229 2005c:54020
29. 1, Proceedings of the American Mathematical Society, 1309 (2002), 2777-2787. MR 1900885 2003a:54002
30. Ma, D. K., The Cantor tree, the ?-property, and Baire function spaces, Proceeedings of the American Mathematical Society, 1193 (1993), 903-913. MR 1165061 93m:54028
31. Malykhin, V. I. and Tironi, G., Weakly Frëchet-Urysohn and Pytkeev spaces, Topology and its Applications, 104 (2000), 181-190. MR 1780904 2001e:54006
32. McCoy, R. A., K-space function spaces, International Journal of Mathematics and Mathematical Sciences, 34 (1980), 701-711. MR 0591780 82d:54012
33. Miller, A. W., A non-hereditary Borel-cover ?-set, Real Analysis Exchange, 29 (2003-2004), 601-606. MR2005g:03079
34. Miller, A. W., On ?'-sets, Topology Proceedings, 28 (2004), no. 1, 179-187. MR 2105456 MR2005h:03093
35. Miller, A. W., The ?-Borel conjecture, Archive for Mathematical Logic, 44 (2005), 425-434. MR 2139770 2005m:03096
36. Miller, A. W., The cardinal characteristics for relative ?-sets, Topology and its Applications, 156 (2009), 872-878. MR 2498919 2010a:54035
37. Miller, A. W., A hodgepodge of sets of reals, Note di Matematica, 27 (2007), Supplemento I, 25-39. MR 2406153 2009e:03087
38. Moore, J. T., A solution of the L-space problem, Journal of the American Mathematical Society, 19 (2006), 717-736. MR 2220104 2008c:54022
39. Nowik, A., Scheepers, M. and Weiss, T., The algebraic sum of sets of real numbers with strong measure zero sets, The Journal of Symbolic Logic, 631 (1998), 301-324. MR 1610427 99c:54049
40. Nyikos, P., Moving-off collections and spaces of continuous functions, unpublished manuscript.
41. Orenshtein, T. and Tsaban, B., Linear s-additivity and some Applications, Transactions of the American Mathematical Society, to appear.
42. Pol, R., A function space C(X) which is weakly Lindelöf but not weakly compactly generated, Studia Mathematicae, 64 (1979), 279-285. MR 0544732 80j:46042
43. Rothberger, F., Eine Verschärfung der Eigenschaft C, Fundamenta Mathematicae, 30 (1938), 50-55.
44. Scheepers, M., Combinatorics of open covers I: Ramsey Theory, Topology and its Applications, 69 (1996), no. 1, 31-62. MR 1378387 97h:90123 (Pubitemid 126665933)
45. Scheepers, M., Combinatorics of open covers VI: Selectors for sequences of dense sets, Quaestiones Mathematicae, 221 (1999), 109-130. MR 1711901 2001j:91031
46. Scheepers, M., Measurable cardinals and the cardinality of Lindelöf spaces, Topology and its Applications, 1579 (2010), 1651-1657. MR 2639831
47. Scheepers, M. and Tall, F. D., Lindelöf indestructibility, topological games and selection principles, Fundamenta Mathematicae, to appear.
48. Sharma, P. L., Some characterizations of W-spaces and w-spaces, General Topology and its Applications, 93 (1978), 289-293. MR 0510910 80a:54046
49. d, Topology and its Applications, 63 (1995), 21-38. MR 1328616 96i:54016
50. Todorcevic, S., Aronszajn orderings, Publicationes de L'Institut Mathëmatique (Nouvelle sërie), 57(71) (1995), 29-46. MR 1387352 98g:0
51. Tsaban, B. and Weiss, T., Products of special sets of real numbers, Real Analysis Exchange, 30 (2004/5), 819-836.
52. Tsaban, B. and Zdomskyy, L., Scales, fields and a problem of Hurewicz, Journal of the European Mathematical Society, 10 (2008), 837-866. MR 2421163 2009j:54037
53. Zdomsky, L., A semifilter approach to selection principles, Commentationes Mathematicae Universitatis Carolinae, 463 (2005), 525-539. MR 2174530 2006g:54028