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: 8

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

Monotone weak Lindelöfness

100%
Bonanzinga M., Cammaroto F., Pansera B.
Open Mathematics
|
2011
|
tom 9
|
nr 3
583-592
EN
The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and subspaces are discussed.
2
Content available remote

On weaker forms of the chain (F) condition and metacompactness-like covering properties in the product spaces

81%
Önal S., Vural Ç.
Open Mathematics
|
2013
|
tom 11
|
nr 9
1635-1642
EN
We introduce the concept of a family of sets generating another family. Then we prove that if X is a topological space and X has W = {W(x): x ∈ X} which is finitely generated by a countable family satisfying (F) which consists of families each Noetherian of ω-rank, then X is metaLindelöf as well as a countable product of them. We also prove that if W satisfies ω-rank (F) and, for every x ∈ X, W(x) is of the form W 0(x) ∪ W 1(x), where W 0(x) is Noetherian and W 1(x) consists of neighbourhoods of x, then X is metacompact.
3
Content available remote

A note on the extent of two subclasses of star countable spaces

81%
Yu Z.
Open Mathematics
|
2012
|
tom 10
|
nr 3
1067-1070
EN
We prove that every Tychonoff strongly monotonically monolithic star countable space is Lindelöf, which solves a question posed by O.T. Alas et al. We also use this result to generalize a metrization theorem for strongly monotonically monolithic spaces. At the end of this paper, we study the extent of star countable spaces with k-in-countable bases, k ∈ ℤ.
4
Content available remote

Remarks on absolutely star countable spaces

81%
Song Y.-K.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1755-1762
EN
We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which is not star countable (hence not absolutely star countable); (4) assuming $$2^{\aleph _0 } = 2^{\aleph _1 }$$, there exists an absolutely star countable normal space having a regular closed subspace which is not star countable (hence not absolutely star countable).
5
Content available remote

Some weak covering properties and infinite games

81%
Sakai M.
Open Mathematics
|
2014
|
tom 12
|
nr 2
322-329
EN
We show that (I) there is a Lindelöf space which is not weakly Menger, (II) there is a Menger space for which TWO does not have a winning strategy in the game Gfin(O,Do). These affirmatively answer questions posed in Babinkostova, Pansera and Scheepers [Babinkostova L., Pansera B.A., Scheepers M., Weak covering properties and infinite games, Topology Appl., 2012, 159(17), 3644–3657]. The result (I) automatically gives an affirmative answer of Wingers’ problem [Wingers L., Box products and Hurewicz spaces, Topology Appl., 1995, 64(1), 9–21], too. The selection principle S1(Do,Do) is also discussed in view of a special base. We show that every subspace of a hereditarily Lindelöf space with an ortho-base satisfies S1(Do,Do).
6
Content available remote

The one-point Lindelöfication of an uncountable discrete space can be surlindelöf

62%
Okunev O.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1750-1754
EN
We prove that the one-point Lindelöfication of a discrete space of cardinality ω 1 is homeomorphic to a subspace of C p (X) for some hereditarily Lindelöf space X if the axiom [...] holds.
7
Content available remote

LΣ(≤ ω)-spaces and spaces of continuous functions

62%
Lara I., Okunev O.
Open Mathematics
|
2010
|
tom 8
|
nr 4
754-762
EN
We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to $$ \mathfrak{c} $$ is an LΣ(≤ ω)-space.
8
Content available remote

Topological spaces compact with respect to a set of filters

52%
Lipparini P.
Open Mathematics
|
2014
|
tom 12
|
nr 7
991-999
EN
If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there is a filter such that sequencewise -compactness is equivalent to F-compactness. If this is the case, and there exists a sequencewise -compact T 1 topological space with more than one point, then F is necessarily an ultrafilter. The particular case of sequential compactness is analyzed in detail.
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.