# On having a countable cover by sets of small local diameter

Studia Mathematica (2000)

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

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topRibarska, 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 -

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