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

Separable reduction theorems by the method of elementary submodels

100%
Cúth M.
Fundamenta Mathematicae
|
2012
|
tom 219
|
nr 3
191-222
EN
We simplify the presentation of the method of elementary submodels and we show that it can be used to simplify proofs of existing separable reduction theorems and to obtain new ones. Given a nonseparable Banach space X and either a subset A ⊂ X or a function f defined on X, we are able for certain properties to produce a separable subspace of X which determines whether A or f has the property in question. Such results are proved for properties of sets: of being dense, nowhere dense, meager, residual or porous, and for properties of functions: of being continuous, semicontinuous or Fréchet differentiable. Our method of creating separable subspaces enables us to combine results, so we easily get separable reductions of properties such as being continuous on a dense subset, Fréchet differentiable on a residual subset, etc. Finally, we show some applications of separable reduction theorems and demonstrate that some results of Zajíček, Lindenstrauss and Preiss hold in the nonseparable setting as well.
2
Content available remote

Rich families and elementary submodels

63%
Cúth M., Kalenda O.
Open Mathematics
|
2014
|
tom 12
|
nr 7
1026-1039
EN
We compare two methods of proving separable reduction theorems in functional analysis - the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density ℵ1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality indexed by ranges of its projections.
3
Content available remote

Note on Bessaga-Klee classification

63%
Cúth M., Kalenda O.
Colloquium Mathematicum
|
2015
|
tom 140
|
nr 1
59-74
EN
We collect several variants of the proof of the third case of the Bessaga-Klee relative classification of closed convex bodies in topological vector spaces. We were motivated by the fact that we have not found anywhere in the literature a complete correct proof. In particular, we point out an error in the proof given in the book of C. Bessaga and A. Pełczyński (1975). We further provide a simplified version of T. Dobrowolski's proof of the smooth classification of smooth convex bodies in Banach spaces which also works in the topological case.
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.