Ball-Complete Sets and Solar Properties of Sets in Asymmetric Spaces

Алимов, А. Р.; Царьков, Игорь Германович

doi:10.1007/s00025-022-01619-2

Search citation statements

Order By: Relevance

Paper Sections

Select...

§ 1 Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

2024

Publication Types

Select...

Article6

Relationship

Self Cite0

Independent6

Authors

Journals

Cited by 18 publications

(1 citation statement)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…) is lower semicontinuous on X (see [7], [8]) and continuous on any finite-dimensional subspace. Given any ε > 0, for each point x of the compact set K, consider a δ x -neighbourhood O δx (x), where δ x ∈ (0, ε/4), of this point such that ϱ(y, M ) < ϱ(x, M ) + ε/4 for all y ∈ O δx (x) (this is possible since the metric function is continuous).…”

Section: § 1 Introductionmentioning

confidence: 99%

Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces

Tsar'kov

2023

Izv. Math.

View full text Add to dashboard Cite

The Michael selection theorem is extended to the case of set-valued mappings with not necessarily convex values. Classical approximation problems on cone-spaces with symmetric and asymmetric seminorms are considered. In particular, conditions for existence of continuous selections for convex subsets of asymmetric spaces are studied. The problem of existence of a Chebyshev centre for a bounded set is solved in a semilinear space consisting of bounded convex sets with Hausdorff semimetric.

show abstract

Section: § 1 Introductionmentioning

confidence: 99%