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

Fundamenta Mathematicae (2011)

- Volume: 215, Issue: 1, page 87-100
- ISSN: 0016-2736

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topA. 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 -

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