On powers of Lindelöf spaces

@article{Gorelic1994,
abstract = {We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space $X$ whose square $X^2$ is again Lindelöf but its cube $X^3$ has a closed discrete subspace of size $\{\mathfrak \{c\}\}^+$, hence the Lindelöf degree $L(X^3) = \{\mathfrak \{c\}\}^+ $. In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space $X$ such that $L(X^n) = \aleph _0$ for all positive integers $n$, but $L(X^\{\aleph _0\}) = \{\mathfrak \{c\}\}^+ = \aleph _2$.},
author = {Gorelic, Isaac},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {forcing; topology; products; Lindelöf; Lindelöf space},
language = {eng},
number = {2},
pages = {383-401},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On powers of Lindelöf spaces},
url = {http://eudml.org/doc/247569},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Gorelic, Isaac
TI - On powers of Lindelöf spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 2
SP - 383
EP - 401
AB - We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space $X$ whose square $X^2$ is again Lindelöf but its cube $X^3$ has a closed discrete subspace of size ${\mathfrak {c}}^+$, hence the Lindelöf degree $L(X^3) = {\mathfrak {c}}^+ $. In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space $X$ such that $L(X^n) = \aleph _0$ for all positive integers $n$, but $L(X^{\aleph _0}) = {\mathfrak {c}}^+ = \aleph _2$.
LA - eng
KW - forcing; topology; products; Lindelöf; Lindelöf space
UR - http://eudml.org/doc/247569
ER -