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: 5

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

Egoroff, σ, and convergence properties in some archimedean vector lattices

100%
Hager A., van Mill J.
Studia Mathematica
|
2015
|
tom 231
|
nr 3
269-285
EN
An archimedean vector lattice A might have the following properties: (1) the sigma property (σ): For each ${aₙ}_{n∈ ℕ} conA⁺$ there are ${λₙ}_{n ∈ ℕ} ⊆ (0,∞)$ and a ∈ A with λₙaₙ ≤ a for each n; (2) order convergence and relative uniform convergence are equivalent, denoted (OC ⇒ RUC): if aₙ ↓ 0 then aₙ → 0 r.u. The conjunction of these two is called strongly Egoroff. We consider vector lattices of the form D(X) (all extended real continuous functions on the compact space X) showing that (σ) and (OC ⇒ RUC) are equivalent, and equivalent to this property of X: (E) the intersection of any sequence of dense cozero-sets contains another. (In case X is zero-dimensional, (E) holds iff the clopen algebra clopX of X is a 'Egoroff Boolean algebra'.) A crucial part of the proof is this theorem about any compact X: For any countable intersection of dense cozero-sets U, there is uₙ ↓ 0 in C(X) with {x ∈ X: uₙ(x) ↓ 0} = U. Then, we make a construction of many new X with (E) (thus, dually, strongly Egoroff D(X)), which can be F-spaces, connected, or zero-dimensional, depending on the input to the construction. This results in many new Egoroff Boolean algebras which are also weakly countably complete.
2
Content available remote

Nonhomogeneity of Remainders, II

100%
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.
3
Content available remote

Notes on Retracts of Coset Spaces

100%
van Mill J., Ridderbos G.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2005
|
tom 53
|
nr 2
169-179
EN
We study retracts of coset spaces. We prove that in certain spaces the set of points that are contained in a component of dimension less than or equal to n, is a closed set. Using our techniques we are able to provide new examples of homogeneous spaces that are not coset spaces. We provide an example of a compact homogeneous space which is not a coset space. We further provide an example of a compact metrizable space which is a retract of a homogeneous compact space, but which is not a retract of a homogeneous metrizable compact space.
4
Content available remote

Sum theorems for Ohio completeness

81%
Basile D., van Mill J., Ridderbos G.
Colloquium Mathematicum
|
2008
|
tom 113
|
nr 1
91-104
EN
We present several sum theorems for Ohio completeness. We prove that Ohio completeness is preserved by taking σ-locally finite closed sums and also by taking point-finite open sums. We provide counterexamples to show that Ohio completeness is preserved neither by taking locally countable closed sums nor by taking countable open sums.
5
Content available remote

Embeddings into 𝓟(ℕ)/fin and extension of automorphisms

61%
Bella A., Dow A., Hart K., Hrusak M., van Mill J., Ursino P.
Fundamenta Mathematicae
|
2002
|
tom 174
|
nr 3
271-284
EN
Given a Boolean algebra 𝔹 and an embedding e:𝔹 → 𝓟(ℕ)/fin we consider the possibility of extending each or some automorphism of 𝔹 to the whole 𝓟(ℕ)/fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.
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.