PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

Fundamenta Mathematicae

2008 | 200 | 2 | 161-184
Tytuł artykułu

Generalized Helly spaces, continuity of monotone functions, and metrizing maps

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given an ordered metric space (in particular, a Banach lattice) E, the generalized Helly space H(E) is the set of all increasing functions from the interval [0,1] to E considered with the topology of pointwise convergence, and E is said to have property (λ) if each of these functions has only countably many points of discontinuity. The main objective of the paper is to study those ordered metric spaces C(K,E), where K is a compact space, that have property (λ). In doing so, the guiding idea comes from the fact that there is a natural one-to-one correspondence between increasing functions f: [0,1] → C(K,E) (with countably many discontinuities) and continuous maps F: K → H(E) (with metrizable ranges). It leads to the investigation of general continuous metrizing maps (those with metrizable ranges), and especially of the so called separately metrizing maps, and the results obtained are then used to derive some permanence properties of the class of spaces C(K,E) with property (λ). For instance, it is shown that if K is the product of compact spaces $K_{j}$ (j ∈ J) such that each of the spaces $C(K_{j},E)$ has property (λ), so does C(K,E); and, for any compact space K, if both C(K) and a Banach lattice E have property (λ), so does C(K,E).
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
161-184
Opis fizyczny
Daty
wydano
2008
Twórcy
autor
• Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
autor
• Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory