On having a countable cover by sets of small local diameter

Nadezhda Ribarska

Studia Mathematica (2000)

  • Volume: 140, Issue: 2, page 99-116
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Ribarska, Nadezhda. "On having a countable cover by sets of small local diameter." Studia Mathematica 140.2 (2000): 99-116. <http://eudml.org/doc/216763>.

@article{Ribarska2000,
abstract = {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.},
author = {Ribarska, Nadezhda},
journal = {Studia Mathematica},
keywords = {countable cover by sets of small local diameter; fragmentability; Kadec renorming; Kadec norm; countable cover by sets of small local -diameter; -SLD property; Kadec-renorming; Hausdorff compacta; -Kadec norm},
language = {eng},
number = {2},
pages = {99-116},
title = {On having a countable cover by sets of small local diameter},
url = {http://eudml.org/doc/216763},
volume = {140},
year = {2000},
}

TY - JOUR
AU - Ribarska, Nadezhda
TI - On having a countable cover by sets of small local diameter
JO - Studia Mathematica
PY - 2000
VL - 140
IS - 2
SP - 99
EP - 116
AB - 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.
LA - eng
KW - countable cover by sets of small local diameter; fragmentability; Kadec renorming; Kadec norm; countable cover by sets of small local -diameter; -SLD property; Kadec-renorming; Hausdorff compacta; -Kadec norm
UR - http://eudml.org/doc/216763
ER -

References

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  15. [15] M. Raja, On topology and renorming of Banach space, C. R. Acad. Bulgare Sci. 52 (1999), 13-16. Zbl0946.46015
  16. [16] M. Raja, Kadec norms and Borel sets in a Banach space, Studia Math. 136 (1999), 1-16. Zbl0935.46021
  17. [17] N. K. Ribarska, Internal characterization of fragmentable spaces, Mathematika 34 (1987), 243-257. Zbl0645.46017
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  19. [19] N. K. Ribarska, A stability property for σ-fragmentability, manuscript, 1996. 

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