# Remainders of metrizable and close to metrizable spaces

Fundamenta Mathematicae (2013)

- Volume: 220, Issue: 1, page 71-81
- ISSN: 0016-2736

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topA. 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 -

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