Σ s -products revisited

Reynaldo Rojas-Hernández

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 2, page 243-255
  • ISSN: 0010-2628

Abstract

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We show that any Σ s -product of at most 𝔠 -many L Σ ( ≤ ω ) -spaces has the L Σ ( ≤ ω ) -property. This result generalizes some known results about L Σ ( ≤ ω ) -spaces. On the other hand, we prove that every Σ s -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every Σ s -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe property by condensations, Topology Proc. 42 (2012), 1–15]. Besides, we prove that if X is a simple Lindelöf Σ -space, then C p ( X ) has the Collins-Roscoe property.

How to cite

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Rojas-Hernández, Reynaldo. "$\Sigma _s$-products revisited." Commentationes Mathematicae Universitatis Carolinae 56.2 (2015): 243-255. <http://eudml.org/doc/270086>.

@article{Rojas2015,
abstract = {We show that any $\Sigma _s$-product of at most $\mathfrak \{c\}$-many $L\Sigma (\le \omega )$-spaces has the $L\Sigma (\le \omega )$-property. This result generalizes some known results about $L\Sigma (\le \omega )$-spaces. On the other hand, we prove that every $\Sigma _s$-product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every $\Sigma _s$-product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe property by condensations, Topology Proc. 42 (2012), 1–15]. Besides, we prove that if $X$ is a simple Lindelöf $\Sigma $-space, then $C_p(X)$ has the Collins-Roscoe property.},
author = {Rojas-Hernández, Reynaldo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\Sigma _s$-product; Lindelöf $\Sigma $-space; $L\Sigma (\le \omega )$-space; monotonically monolithic space; Collins-Roscoe space; function space; simple space},
language = {eng},
number = {2},
pages = {243-255},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$\Sigma _s$-products revisited},
url = {http://eudml.org/doc/270086},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Rojas-Hernández, Reynaldo
TI - $\Sigma _s$-products revisited
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 2
SP - 243
EP - 255
AB - We show that any $\Sigma _s$-product of at most $\mathfrak {c}$-many $L\Sigma (\le \omega )$-spaces has the $L\Sigma (\le \omega )$-property. This result generalizes some known results about $L\Sigma (\le \omega )$-spaces. On the other hand, we prove that every $\Sigma _s$-product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every $\Sigma _s$-product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe property by condensations, Topology Proc. 42 (2012), 1–15]. Besides, we prove that if $X$ is a simple Lindelöf $\Sigma $-space, then $C_p(X)$ has the Collins-Roscoe property.
LA - eng
KW - $\Sigma _s$-product; Lindelöf $\Sigma $-space; $L\Sigma (\le \omega )$-space; monotonically monolithic space; Collins-Roscoe space; function space; simple space
UR - http://eudml.org/doc/270086
ER -

References

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