We prove that if X is a strongly zero-dimensional space, then for every locally compact second-countable space M, C p(X, M) is a continuous image of a closed subspace of C p(X). It follows in particular, that for strongly zero-dimensional spaces X, the Lindelöf number of C p(X)×C p(X) coincides with the Lindelöf number of C p(X). We also prove that l(C p(X n)κ) ≤ l(C p(X)κ) whenever κ is an infinite cardinal and X is a strongly zero-dimensional union of at most κcompact subspaces.
@article{bwmeta1.element.doi-10_2478_s11533-011-0050-y,
author = {Oleg Okunev},
title = {The Lindel\"of number of C p(X)$\times$C p(X) for strongly zero-dimensional X},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {978-983},
zbl = {1245.54018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0050-y}
}
Oleg Okunev. The Lindelöf number of C p(X)×C p(X) for strongly zero-dimensional X. Open Mathematics, Tome 9 (2011) pp. 978-983. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0050-y/
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