Vector lattice covers of ideals and bands in Pre-Riesz spaces
| Autor: | Anke Kalauch, Helena Malinowski |
|---|---|
| Přispěvatelé: | 31579922 - Malinowski, Helena |
| Rok vydání: | 2018 |
| Předmět: |
Extension band
Pure mathematics High Energy Physics::Lattice Mathematics::Classical Analysis and ODEs 0211 other engineering and technologies 02 engineering and technology Space (mathematics) 01 natural sciences Mathematics (miscellaneous) Lattice (order) FOS: Mathematics 0101 mathematics Pre-Riesz space Order ideal Extension ideal Pervasive Mathematics Mathematics::Functional Analysis 021103 operations research Order ideal band pre-Riesz space ordered vector space vector lattice cover order dense extension ideal extension band pervasive Vector lattice cover Order dense 010102 general mathematics Order (ring theory) Ordered vector space 46A40 06F20 Functional Analysis (math.FA) Band Mathematics - Functional Analysis Cover (topology) Vector space |
| Zdroj: | Quaestiones Mathematicae; Vol 42, No 7 (2019); 919–937 |
| ISSN: | 1727-933X 1607-3606 |
| Popis: | Pre-Riesz spaces are ordered vector spaces which can be order densely embedded into vector lattices, their so-called vector lattice covers. Given a vector lattice cover Y for a pre-Riesz space X, we address the question how to find vector lattice covers for subspaces of X, such as ideals and bands. We provide conditions such that for a directed ideal I in X its smallest extension ideal in Y is a vector lattice cover. We show a criterion for bands in X and their extension bands in Y as well. Moreover, we state properties of ideals and bands in X which are generated by sets, and of their extensions in Y .Key words: Order ideal, band, pre-Riesz space, ordered vector space, vector lattice cover, order dense, extension ideal, extension band, pervasive. |
| Databáze: | OpenAIRE |
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