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: 3

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

Approximation theorems for compactifications

100%
Mine K.
Colloquium Mathematicum
|
2011
|
tom 122
|
nr 1
93-101
EN
We shall show several approximation theorems for the Hausdorff compactifications of metrizable spaces or locally compact Hausdorff spaces. It is shown that every compactification of the Euclidean n-space ℝⁿ is the supremum of some compactifications homeomorphic to a subspace of $ℝ^{n+1}$. Moreover, the following are equivalent for any connected locally compact Hausdorff space X: (i) X has no two-point compactifications, (ii) every compactification of X is the supremum of some compactifications whose remainder is homeomorphic to the unit closed interval or a singleton, (iii) every compactification of X is the supremum of some singular compactifications. We shall also give a necessary and sufficient condition for a compactification to be approximated by metrizable (or Smirnov) compactifications.
2
Content available remote

Open Subsets of LF-spaces

63%
Mine K., Sakai K.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2008
|
tom 56
|
nr 1
25-37
EN
Let F = ind lim Fₙ be an infinite-dimensional LF-space with density dens F = τ ( ≥ ℵ ₀) such that some Fₙ is infinite-dimensional and dens Fₙ = τ. It is proved that every open subset of F is homeomorphic to the product of an ℓ₂(τ)-manifold and $ℝ^∞ = ind lim ℝ ⁿ$ (hence the product of an open subset of ℓ₂(τ) and $ℝ^∞$). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.
3
Content available remote

Hyperspaces of Finite Sets in Universal Spaces for Absolute Borel Classes

51%
Mine K., Sakai K., Yaguchi M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2005
|
tom 53
|
nr 4
409-419
EN
By Fin(X) (resp. $Fin^{k}(X)$), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ₂(τ) be the Hilbert space with weight τ and $ℓ₂^{f}(τ)$ the linear span of the canonical orthonormal basis of ℓ₂(τ). It is shown that if $E = ℓ₂^{f}(τ)$ or E is an absorbing set in ℓ₂(τ) for one of the absolute Borel classes $𝔞_α(τ)$ and $𝔐_α(τ)$ of weight ≤ τ (α > 0) then Fin(E) and each $Fin^{k}(E)$ are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic to E and each $Fin^{k}(X)$ is a connected E-manifold.
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.