A nice class extracted from C p -theory

Vladimir Vladimirovich Tkachuk

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 3, page 503-513
  • ISSN: 0010-2628

Abstract

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We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, ω -stable and ω -monolithic. It is also established that any Sokolov compact space X is Fréchet-Urysohn and the space C p ( X ) is Lindelöf. We prove that any Sokolov space with a G δ -diagonal has a countable network and obtain some cardinality restrictions on subsets of small pseudocharacter lying in Σ -products of cosmic spaces.

How to cite

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Tkachuk, Vladimir Vladimirovich. "A nice class extracted from $C_p$-theory." Commentationes Mathematicae Universitatis Carolinae 46.3 (2005): 503-513. <http://eudml.org/doc/249567>.

@article{Tkachuk2005,
abstract = {We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, $\omega $-stable and $\omega $-monolithic. It is also established that any Sokolov compact space $X$ is Fréchet-Urysohn and the space $C_p(X)$ is Lindelöf. We prove that any Sokolov space with a $G_\delta $-diagonal has a countable network and obtain some cardinality restrictions on subsets of small pseudocharacter lying in $\Sigma $-products of cosmic spaces.},
author = {Tkachuk, Vladimir Vladimirovich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Corson compact space; Sokolov space; extent; $\omega $-monolithic space; $\Sigma $-products; Corson compact space; Sokolov space; extent; -monolithic space; -products},
language = {eng},
number = {3},
pages = {503-513},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A nice class extracted from $C_p$-theory},
url = {http://eudml.org/doc/249567},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Tkachuk, Vladimir Vladimirovich
TI - A nice class extracted from $C_p$-theory
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 3
SP - 503
EP - 513
AB - We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, $\omega $-stable and $\omega $-monolithic. It is also established that any Sokolov compact space $X$ is Fréchet-Urysohn and the space $C_p(X)$ is Lindelöf. We prove that any Sokolov space with a $G_\delta $-diagonal has a countable network and obtain some cardinality restrictions on subsets of small pseudocharacter lying in $\Sigma $-products of cosmic spaces.
LA - eng
KW - Corson compact space; Sokolov space; extent; $\omega $-monolithic space; $\Sigma $-products; Corson compact space; Sokolov space; extent; -monolithic space; -products
UR - http://eudml.org/doc/249567
ER -

References

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