Remainders of metrizable spaces and a generalization of Lindelöf Σ-spaces

A. V. Arhangel'skii. "Remainders of metrizable spaces and a generalization of Lindelöf Σ-spaces." Fundamenta Mathematicae 215.1 (2011): 87-100. <http://eudml.org/doc/282733>.

@article{A2011,
abstract = {We establish some new properties of remainders of metrizable spaces. In particular, we show that if the weight of a metrizable space X does not exceed $2^\{ω\}$, then any remainder of X in a Hausdorff compactification is a Lindelöf Σ-space. An example of a metrizable space whose remainder in some compactification is not a Lindelöf Σ-space is given. A new class of topological spaces naturally extending the class of Lindelöf Σ-spaces is introduced and studied. This leads to the following theorem: if a metrizable space X has a remainder Y with a $G_\{δ\}$-diagonal, then both X and Y are separable and metrizable. Some new results on remainders of topological groups are also established.},
author = {A. V. Arhangel'skii},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {1},
pages = {87-100},
title = {Remainders of metrizable spaces and a generalization of Lindelöf Σ-spaces},
url = {http://eudml.org/doc/282733},
volume = {215},
year = {2011},
}

TY - JOUR
AU - A. V. Arhangel'skii
TI - Remainders of metrizable spaces and a generalization of Lindelöf Σ-spaces
JO - Fundamenta Mathematicae
PY - 2011
VL - 215
IS - 1
SP - 87
EP - 100
AB - We establish some new properties of remainders of metrizable spaces. In particular, we show that if the weight of a metrizable space X does not exceed $2^{ω}$, then any remainder of X in a Hausdorff compactification is a Lindelöf Σ-space. An example of a metrizable space whose remainder in some compactification is not a Lindelöf Σ-space is given. A new class of topological spaces naturally extending the class of Lindelöf Σ-spaces is introduced and studied. This leads to the following theorem: if a metrizable space X has a remainder Y with a $G_{δ}$-diagonal, then both X and Y are separable and metrizable. Some new results on remainders of topological groups are also established.
LA - eng
UR - http://eudml.org/doc/282733
ER -