Remainders of metrizable and close to metrizable spaces

A. V. Arhangel'skii. "Remainders of metrizable and close to metrizable spaces." Fundamenta Mathematicae 220.1 (2013): 71-81. <http://eudml.org/doc/283318>.

@article{A2013,
abstract = {We continue the study of remainders of metrizable spaces, expanding and applying results obtained in [Fund. Math. 215 (2011)]. Some new facts are established. In particular, the closure of any countable subset in the remainder of a metrizable space is a Lindelöf p-space. Hence, if a remainder of a metrizable space is separable, then this remainder is a Lindelöf p-space. If the density of a remainder Y of a metrizable space does not exceed $2^\{ω\}$, then Y is a Lindelöf Σ-space. We also show that many of the theorems on remainders of metrizable spaces can be extended to paracompact p-spaces or to spaces with a σ-disjoint base. We also extend to remainders of metrizable spaces the well known theorem on metrizability of compacta with a point-countable base.},
author = {A. V. Arhangel'skii},
journal = {Fundamenta Mathematicae},
keywords = {metrizable; paracompact -space; Lindelöf -space; Lindelöf -space; symmetrizable; countable type},
language = {eng},
number = {1},
pages = {71-81},
title = {Remainders of metrizable and close to metrizable spaces},
url = {http://eudml.org/doc/283318},
volume = {220},
year = {2013},
}

TY - JOUR
AU - A. V. Arhangel'skii
TI - Remainders of metrizable and close to metrizable spaces
JO - Fundamenta Mathematicae
PY - 2013
VL - 220
IS - 1
SP - 71
EP - 81
AB - We continue the study of remainders of metrizable spaces, expanding and applying results obtained in [Fund. Math. 215 (2011)]. Some new facts are established. In particular, the closure of any countable subset in the remainder of a metrizable space is a Lindelöf p-space. Hence, if a remainder of a metrizable space is separable, then this remainder is a Lindelöf p-space. If the density of a remainder Y of a metrizable space does not exceed $2^{ω}$, then Y is a Lindelöf Σ-space. We also show that many of the theorems on remainders of metrizable spaces can be extended to paracompact p-spaces or to spaces with a σ-disjoint base. We also extend to remainders of metrizable spaces the well known theorem on metrizability of compacta with a point-countable base.
LA - eng
KW - metrizable; paracompact -space; Lindelöf -space; Lindelöf -space; symmetrizable; countable type
UR - http://eudml.org/doc/283318
ER -