On some convergence approach structures on hyperspaces
Applied General Topology, cilt.27, sa.2, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 27 Sayı: 2
- Basım Tarihi: 2026
- Doi Numarası: 10.4995/agt.25805
- Dergi Adı: Applied General Topology
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals, DIALNET, Academic Search Ultimate (EBSCO)
- Anahtar Kelimeler: convergence approach spaces, Fell structure, Kuratowski convergence
- Ankara Üniversitesi Adresli: Evet
Özet
In the context of the category Cap of convergence approach spaces and contractions, we introduce and study approach analogs of the upper and lower Kuratowski conver-gences, upper-Fell and Fell topologies on the set of closed subsets of the coreflection on the category Conv of convergence spaces of a convergence approach space. In particular, over a pre-approach space, the Conv-coreflection of the lower Kuratowski convergence approach structure is the lower Kuratowski convergence associated with the Conv-coreflection of the base space, while the Conv-reflection is the lower Kura-towski convergence associated with the Conv-reflection. The Conv-coreflection of the upper Kuratowski convergence approach is the upper Kuratowski convergence associated with the Conv-reflection of the base space, while the Conv-reflection is the upper Kuratowski convergence associated with the Conv-coreflection of the base space. We show that, over an approach space, the lower Kuratowski convergence approach structure is in fact an approach structure that coincides with the ∨-Vietoris approach structure introduced by Lowen and his collaborators, though it may be strictly finer over a general convergence approach space. We show that the upper Fell convergence approach structure is a non-Archimedean approach structure coarser than the upper Kuratowski convergence approach, but finer than the upper Fell approach structure introduced by the first and third author. We also obtain a Cap abstraction of the classical result that if the upper Kuratowski convergence over a topological space is pretopo-logical, then it is also topological.