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2000 | 140 | 2 | 99-116
Tytuł artykułu

On having a countable cover by sets of small local diameter

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A characterization of topological spaces admitting a countable cover by sets of small local diameter close in spirit to known characterizations of fragmentability is obtained. It is proved that if X and Y are Hausdorff compacta such that C(X) has an equivalent p-Kadec norm and $C_p(Y)$ has a countable cover by sets of small local norm diameter, then $C_p(X×Y)$ has a countable cover by sets of small local norm diameter as well.
Czasopismo
Rocznik
Tom
140
Numer
2
Strony
99-116
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-12-22
poprawiono
2000-01-13
Twórcy
  • Department of Mathematics and Informatics, University of Sofia, J. Bourchier boul. 5a, 1164 Sofia, Bulgaria, ribarska@fmi.uni-sofia.bg
Bibliografia
  • [1] R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Longman, 1993.
  • [2] E G. E. Edgar, Measurability in a Banach space, Indiana Univ. Math. J. 28 (1979), 559-579.
  • [3] R. Engelking, General Topology, PWN, Warszawa, 1985.
  • [4] G G. Gruenhage, A note on Gul'ko compact spaces, Proc. Amer. Math. Soc. 100 (1987), 371-376.
  • [5] H R. W. Hansell, Descriptive sets and the topology of nonseparable Banach spaces, preprint (1989).
  • [6] J. E. Jayne, I. Namioka and C. A. Rogers, σ-fragmentable Banach spaces, Mathematika 39 (1992), 161-188 and 197-215.
  • [7] J. E. Jayne, I. Namioka and C. A. Rogers, Topological properties of Banach spaces, Proc. London Math. Soc. 66 (1993), 651-672.
  • [8] J. E. Jayne, I. Namioka and C. A. Rogers, Continuous functions on products of compact Hausdorff spaces, to appear.
  • [9] J. E. Jayne and C. E. Rogers, Borel selectors for upper semicontinuous set-valued maps, Acta Math. 155 (1985), 41-79.
  • [10] P. S. Kenderov and W. Moors, Fragmentability and sigma-fragmentability of Banach spaces, J. London Math. Soc. 60 (1999), 203-223.
  • [11] A. Moltó, J. Orihuela and S. Troyanski, Locally uniformly rotund renorming and fragmentability, Proc. London Math. Soc. 75 (1997), 619-640.
  • [12] A. Moltó, J. Orihuela, S. Troyanski and M. Valdivia, On weakly locally uniformly rotund Banach spaces, J. Funct. Anal. 163 (1999), 252-271.
  • [13] M W. B. Moors, manuscript, 1997.
  • [14] I. Namioka and R. Pol, Sigma-fragmentability of mappings into $C_p(K)$, Topology Appl. 89 (1998), 249-263.
  • [15] M. Raja, On topology and renorming of Banach space, C. R. Acad. Bulgare Sci. 52 (1999), 13-16.
  • [16] M. Raja, Kadec norms and Borel sets in a Banach space, Studia Math. 136 (1999), 1-16.
  • [17] N. K. Ribarska, Internal characterization of fragmentable spaces, Mathematika 34 (1987), 243-257.
  • [18] N. K. Ribarska, A Radon-Nikodym compact which is not a Gruenhage space, C. R. Acad. Bulgare Sci. 41 (1988), 9-11.
  • [19] N. K. Ribarska, A stability property for σ-fragmentability, manuscript, 1996.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv140i2p99bwm
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