A selection of recent results and problems in Cp-theory

Topology and its Applications

Volumn 154, Issue 12, 2007, Pages 2465-2493

  Tkachuk, V V ^a  

^a DEPARTAMENTO DE QUÍMICA   (Mexico)

Author keywords

Compact space; Corson compact; Countably compact spaces; d separable space; D space; Eberlein compact; Gul'ko space; l equivalency; Lindel f property; Lindel f property; Neighborhood assignments; Pseudocompact spaces; Sokolov space; t equivalency

Indexed keywords

EID: 34249902062     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2007.03.013     Document Type: Article

References (100)

1. Alster K., and Pol R. On function spaces of compact subspaces of Σ-products of the real line. Fund. Math. 107 (1980) 135-143
2. Amir D., and Lindenstrauss J. The structure of weakly compact sets in Banach spaces. Ann. of Math. 88 1 (1968) 35-46
3. Arhangel'skii A.V. On some topological spaces occurring in functional analysis. Uspekhi Mat. Nauk 31 5 (1976) 17-32 (in Russian)
4. Arhangel'skii A.V. Structure and classification of topological spaces and cardinal invariants. Uspekhi Mat. Nauk 33 6 (1978) 29-84 (in Russian)
5. Arhangel'skii A.V. On d-separable spaces. In: Alexandroff P.S. (Ed). Proceedings of the Seminar on General Topology (1981), Mosk. Univ. P.H. 3-8
6. Arhangel'skii A.V. On linear homeomorphisms of function spaces. Dokl. AN SSSR 264 6 (1982) 1289-1292 (in Russian)
7. p (X). In: Novak J. (Ed). Proc. Fifth Prague Topol. Symp. General Topology and its Relations to Modern Analysis and Algebra vol. V (1983), Heldermann Verlag, Berlin 24-36
8. p-theory. Questions Answers Gen. Topology 5 (1987) 1-109
9. p-theory. In: Frolik Z. (Ed). Proc. Sixth Prague Topol. Symp. General Topology and its Relations to Modern Analysis and Algebra vol. VI (1988), Heldermann Verlag, Berlin 11-31
10. p-theory. Open Problems in Topology (1990), North-Holland, Amsterdam 603-615
11. Arhangel'skii A.V. Topological Function Spaces (1992), Kluwer Acad. Publ., Dordrecht
12. Arhangel'skii{dotless}̌ A.V. The general concept of cleavability of a topological space. Topology Appl. 44 (1992) 27-36
13. p-theory. In: Hušek M., and van Mill J. (Eds). Recent Progress in General Topology (1992), Elsevier S.P. 1-56
14. Arhangel'skii{dotless}̌ A.V. A survey of cleavability. Topology Appl. 54 (1993) 141-163
15. Arhangel'skii{dotless}̌ A.V. A generic theorem in the theory of cardinal invariants of topological spaces. Comment. Math. Univ. Carolinae 36 2 (1995) 303-325
16. Arhangel'skii{dotless}̌ A.V., and Buzyakova R.Z. Addition theorems and D-spaces. Comment. Math. Univ. Carolinae 43 4 (2002) 653-663
17. X. Proc. Amer. Math. Soc. 127 8 (1999) 2497-2504
18. Arhangel'skii A.V., and Shakhmatov D.B. Splittable spaces and questions of functions approximations. Proceedings of the Fifth Tyraspol Symposium on General Topology and its Applications, Kishinev (1985), Shtiintsa 10-11 (in Russian)
19. Arhangel'skii A.V., and Shakhmatov D.B. On pointwise approximation of arbitrary functions by countable families of continuous functions. Trudy Sem. I.G. Petrovskogo 13 (1988) 206-227 (in Russian)
20. M.O. Asanov, On cardinal invariants of spaces of continuous functions, Modern Topology and Set Theory, Izhevsk, 1979, pp. 8-12 (in Russian)
21. Baturov D.P. On subspaces of function spaces. Vestnik MGU Mat. Mech. 42 4 (1987) 66-69 (in Russian)
22. Borges C.R., and Wehrly A.C. A study of D-spaces. Topology Proc. 16 (1991) 7-15
23. Buzyakova R.Z. On D-property of strong Σ-spaces. Comment. Math. Univ. Carolinae 43 3 (2002) 493-495
24. p's. Comment. Math. Univ. Carolinae 45 1 (2004) 145-151
25. Buzyakova R.Z. On cleavability of continua over LOTS. Proc. Amer. Math. Soc. 132 7 (2004) 2171-2181
26. Buzyakova R.Z. Hereditary D-property of function spaces over compacta. Proc. Amer. Math. Soc. 132 11 (2004) 3433-3439
27. R.Z. Buzyakova, Function spaces over GO spaces, Part I, preprint
28. p (X). Topology Proc. 24 (1999) 89-102
29. Cascales B., and Orihuela J. On compactness in locally convex spaces. Math. Z. 195 (1987) 365-381
30. Cascales B., and Orihuela J. A sequential property of set-valued maps. J. Math. Anal. Appl. 156 1 (1991) 86-100
31. Christensen J.P.R. Topology and Borel Structure. Math. Studies vol. 10 (1974), North-Holland, Amsterdam
32. Ciesielski K. L-space without any uncountable 0-dimensional subspace. Fund. Math. 125 (1985) 231-235
33. λ without dense totally disconnected subsets. Fund. Math. 142 (1993) 85-88
34. Corson H.H. The weak topology of a Banach space. Trans. Amer. Math. Soc. 101 (1961) 1-15
35. van Douwen E.K. Simultaneous linear extensions of continuous functions. Gen. Topology Appl. 5 (1975) 297-319
36. van Douwen E.K., and Lutzer D.J. A note on paracompactness in generalized ordered spaces. Proc. Amer. Math. Soc. 125 (1997) 1237-1245
37. van Douwen E.K., and Pfeffer W.F. Some properties of the Sorgenfrey line and related spaces. Pacific J. Math. 81 2 (1979) 371-377
38. Eisworth T. On D-spaces. Open Problems in Topology II (2007), Elsevier, Amsterdam in press
39. Engelking R. General Topology (1977), PWN, Warszawa
40. Fabian M. Gateaux Differentiability of Convex Functions and Topology, Weak Asplund Spaces (1997), Wiley, New York
41. Gerlits J., and Nagy Zs. Some properties of C (X) I. Topology Appl. 14 2 (1982) 151-161
42. Gerlits J., Nagy Z., and Szentmiklóssy Z. Some convergence properties in function spaces. General Topology and its Relation to Modern Analysis and Algebra (1988), Heldermann, Berlin 211-222
43. Gruenhage G. Infinite games and generalizations of first countable spaces. Gen. Topology Appl. 6 (1976) 339-352
44. 2 \ Δ, W-sets, and compact subsets of Σ-products. Topology Appl. 17 (1984) 287-304
45. Gruenhage G. Spaces having a small diagonal. Topology Appl. 122 2002 (1984) 183-200
46. Gruenhage G. A note on D-spaces. Topology Appl. 153 (2006) 2229-2240
47. Gul'ko S.P. On the properties of some function spaces. Soviet Math. Dokl. 19 6 (1978) 1420-1424
48. Gul'ko S.P. On the structure of spaces of continuous functions and their complete paracompactness. Russian Math. Surv. 34 6 (1979) 36-44
49. Gul'ko S.P. On properties of function spaces. A Seminar of General Topology (1981), Moscow University P.H., Moscow 8-41 (in Russian)
50. Gul'ko S.P., and Khmyleva T.E. The compactness is not preserved by the relation of t-equivalence. Mat. Zametki 39 6 (1986) 895-903 (in Russian)
51. Hodel R.E. On a theorem of Arhangel'skii concerning Lindelöf p-spaces. Canadian J. Math. 27 (1975) 459-468
52. Hodel R.E. Cardinal functions I. In: Kunen K., and Vaughan J.E. (Eds). Handbook of Set-Theoretic Topology (1984), North-Holland, Amsterdam 1-61
53. Jardón D. Weakly Eberlein compact spaces. Topology Proc. 26 (2001-2002) 695-707
54. Jardón D., and Tkachuk V.V. Ultracompleteness in Eberlein-Grothendieck spaces. Bol. Soc. Mat. Mexicana 10 3 (2004) 209-218
55. I. Juhász, Cardinal Functions in Topology-Ten Years Later, Mathematical Centre Tracts 123, Amsterdam, 1980
56. p (X), preprint
57. p (X) and calibers. Canadian Math. Bull. 35 4 (1992) 497-502
58. Leiderman A.G. On dense metrizable subspaces of Corson compacta. Mat. Zametki 38 2 (1985) 440-449 (in Russian)
59. Lutzer D.J., and McCoy R.A. Category in function spaces I. Pacific J. Math. 90 1 (1980) 145-168
60. p (X) imply discreteness of X, submitted for publication
61. Malykhin V.I. On dense subspaces of topological spaces. General Topology; Mappings of Topological Spaces, Proceedings of Seminar on General Topology (1986), Moscow Univ. P.H. 65-76 (in Russian)
62. Marciszewski W. Function spaces. In: Hušek M., and van Mill J. (Eds). Recent Progress in General Topology II (2002), Elsevier Sci. B.V., Amsterdam 345-369
63. McCoy R.A., and Ntantu I. Topological Properties of Spaces of Continuous Functions. Lecture Notes in Math. vol. 1315 (1988), Springer, Berlin
64. van Mill J. The Infinite-Dimensional Topology of Function Spaces. North-Holland Math. Library vol. 64 (2002), Elsevier, Amsterdam
65. L.B. Nakhmanson, The Lindelöf property in function spaces, in: V Tiraspol Symposium on Topology and its Applications, Kishinev, 1985, p. 183 (in Russian)
66. Okunev O.G. A method for constructing examples of M-equivalent spaces. Topology Appl. 36 (1990) 157-171
67. Okunev O.G. On Lindelöf Σ-spaces of continuous functions in the pointwise topology. Topology Appl. 49 2 (1993) 149-166
68. Okunev O.G. Tightness of compact spaces is preserved by the t-equivalence relation. Comment. Math. Univ. Carolinae 43 2 (2002) 335-342
69. Okunev O.G. Fréchet property in compact spaces is not preserved by M-equivalence. Comment. Math. Univ. Carolinae 46 4 (2005) 747-749
70. p (X)) = ω do not imply countable network weight in X. Acta Math. Hungar. 90 1-2 (2001) 119-132
71. Pytkeev E.G. On Fréchet-Urysohn property of spaces of continuous functions, Trudy Math. Inst. RAN 193 (1992) 156-161 (in Russian)
72. Pytkeev E.G. On the tightness of spaces of continuous functions. Uspekhi Mat. Nauk 37 1 (1982) 157-158 (in Russian)
73. Reznichenko E.A. Normality and collectionwise normality in function spaces. Moscow Univ. Math. Bull. 45 6 (1990) 25-26
74. p (X) is σ-countably compact?. Vestnik MGU, Math. Mech. 41 1 (1986) 70-72 (in Russian)
75. Shapirovsky B.E. Cardinal invariants in compact spaces. In: Alexandroff P.S. (Ed). Seminar Gen. Topology (1981), Moscow Univ. P.H., Moscow 162-187 (in Russian)
76. Sipacheva O.V. The structure of iterated function spaces in the topology of pointwise convergence for Eberlein compacta. Mat. Zametki 47 3 (1990) 91-99 (in Russian)
77. Sokolov G.A. On some classes of compact spaces lying in Σ-products. Comment. Math. Univ. Carolinae 25 2 (1984) 219-231
78. Sokolov G.A. On Lindelöf spaces of continuous functions. Mat. Zametki 39 6 (1986) 887-894 (in Russian)
79. Sokolov G.A. Lindelöf property and the iterated continuous function spaces. Fund. Math. 143 (1993) 87-95
80. Talagrand M. Sur une conjeture de H.H. Corson. Bull. Sci. Math. 99 2 (1975) 211-212
81. Talagrand M. Espaces de Banach faiblement K-analytiques. Ann. of Math. 110 3 (1979) 407-438
82. Tkachenko M.G. On continuous images of dense subspaces of topological products. Uspekhi Mat. Nauk 34 6 (1979) 199-202 (in Russian)
83. Tkachenko M.G. On continuous images of dense subspaces of Σ-products of metrizable compacta. Siberian Math. J. 23 3 (1982) 198-207 (in Russian)
84. Tkachenko M.G., and Tkachuk V.V. Dyadicity index and metrizability of compact continuous images of function spaces. Topology Appl. 149 (2005) 243-257
85. Tkachuk V.V. On a method of constructing examples of M-equivalent spaces. Uspekhi Mat. Nauk 38 6 (1983) 127-128 (in Russian)
86. p-functor and cardinal invariants of Souslin number type. Mat. Zametki 37 3 (1985) 441-451 (in Russian)
87. p (X). Comment. Math. Univ. Carolinae 27 2 (1986) 267-276
88. p (X): decomposition into a countable union of bounded subspaces and completeness properties. Topology Appl. 22 3 (1986) 241-254
89. Tkachuk V.V. A note on splittable spaces. Comment. Math. Univ. Carolinae 33 3 (1992) 551-555
90. p (X). Trans. Moscow Math. Soc. 55 (1994) 239-248
91. Tkachuk V.V. Behaviour of the Lindelöf Σ-property in iterated function spaces. Topology Appl. 107 (2000) 297-305
92. p (X) together with countable spread of X implies X is cosmic. New Zealand J. Math. 30 (2001) 93-101
93. Tkachuk V.V. Properties of function spaces reflected by uniformly dense subspaces. Topology Appl. 132 (2003) 183-193
94. Tkachuk V.V. Point-countable π-bases in first countable and similar spaces. Fund. Math. 186 (2005) 55-69
95. p (X) is dominated by irrationals if and only if it is K-analytic. Acta Math. Hungar. 107 4 (2005) 261-273
96. p-theory. Comment. Math. Univ. Carolinae 46 3 (2005) 503-513
97. Tkachuk V.V. Function spaces and d-separability. Quaestiones Math. 28 (2005) 409-424
98. Tkachuk V.V. Condensing function spaces into Σ-products of real lines. Houston J. Math. 33 1 (2007) 209-228
99. de la Vega R., and Kunen K. A compact homogeneous S-space. Topology Appl. 136 (2004) 123-127
100. Yaschenko I.V. On the monotone normality of functional spaces. Moscow Univ. Math. Bull. 49 3 (1994) 62-63