Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 4

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

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

100%
Arhangel'skii A.
Fundamenta Mathematicae
|
2011
|
tom 215
|
nr 1
87-100
EN
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.
2
Content available remote

Remainders of metrizable and close to metrizable spaces

100%
Arhangel'skii A.
Fundamenta Mathematicae
|
2013
|
tom 220
|
nr 1
71-81
EN
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.
3
Content available remote

A study of remainders of topological groups

100%
Arhangel'skii A.
Fundamenta Mathematicae
|
2009
|
tom 203
|
nr 2
165-178
EN
Some duality theorems relating properties of topological groups to properties of their remainders are established. It is shown that no Dowker space can be a remainder of a topological group. Perfect normality of a remainder of a topological group is consistently equivalent to hereditary Lindelöfness of this remainder. No L-space can be a remainder of a non-locally compact topological group. Normality is equivalent to collectionwise normality for remainders of topological groups. If a non-locally compact topological group G has a hereditarily Lindelöf remainder, then G is separable and metrizable. We also present several other criteria for a topological group G to be separable and metrizable. Two of them are of general nature and depend heavily on a new criterion for Lindelöfness of a topological group in terms of remainders. One of them generalizes a theorem of the author [Topology Appl. 150 (2005)] as follows: a topological group G is separable and metrizable if and only if some remainder of G has locally a $G_δ$-diagonal. We also study how close are the topological properties of topological groups that have homeomorphic remainders.
4
Content available remote

Nonhomogeneity of Remainders, II

63%
Arhangel'skii A., van Mill J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2015
|
tom 63
|
nr 1
67-71
EN
We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.