Čech-completeness and ultracompleteness in “nice spaces”
Miguel López de Luna; Vladimir Vladimirovich Tkachuk
Commentationes Mathematicae Universitatis Carolinae (2002)
- Volume: 43, Issue: 3, page 515-524
- ISSN: 0010-2628
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topde Luna, Miguel López, and Tkachuk, Vladimir Vladimirovich. "Čech-completeness and ultracompleteness in “nice spaces”." Commentationes Mathematicae Universitatis Carolinae 43.3 (2002): 515-524. <http://eudml.org/doc/249005>.
@article{deLuna2002,
abstract = {We prove that if $X^n$ is a union of $n$ subspaces of pointwise countable type then the space $X$ is of pointwise countable type. If $X^\omega $ is a countable union of ultracomplete spaces, the space $X^\omega $ is ultracomplete. We give, under CH, an example of a Čech-complete, countably compact and non-ultracomplete space, giving thus a partial answer to a question asked in [BY2].},
author = {de Luna, Miguel López, Tkachuk, Vladimir Vladimirovich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ultracompleteness; Čech-completeness; countable type; pointwise countable type; ultracomplete space; Čech-complete space; countable type; pointwise countable type; additive property},
language = {eng},
number = {3},
pages = {515-524},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Čech-completeness and ultracompleteness in “nice spaces”},
url = {http://eudml.org/doc/249005},
volume = {43},
year = {2002},
}
TY - JOUR
AU - de Luna, Miguel López
AU - Tkachuk, Vladimir Vladimirovich
TI - Čech-completeness and ultracompleteness in “nice spaces”
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 3
SP - 515
EP - 524
AB - We prove that if $X^n$ is a union of $n$ subspaces of pointwise countable type then the space $X$ is of pointwise countable type. If $X^\omega $ is a countable union of ultracomplete spaces, the space $X^\omega $ is ultracomplete. We give, under CH, an example of a Čech-complete, countably compact and non-ultracomplete space, giving thus a partial answer to a question asked in [BY2].
LA - eng
KW - ultracompleteness; Čech-completeness; countable type; pointwise countable type; ultracomplete space; Čech-complete space; countable type; pointwise countable type; additive property
UR - http://eudml.org/doc/249005
ER -
References
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