A reverse viewpoint on the upper semicontinuity of multivalued maps

Title:

A reverse viewpoint on the upper semicontinuity of multivalued maps

Creator:

Fenille, Marcio Colombo

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c77d74bf-813d-4fd3-a153-8cd7247db880
uuid:c77d74bf-813d-4fd3-a153-8cd7247db880
doi:10.21136/MB.2013.143514

Subject:

multivalued map, power set, upper semicontinuity, and upper semifinite topology

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

For a multivalued map ϕ: Y ⊸ (X, τ ) between topological spaces, the upper semifinite topology A(τ ) on the power set A(X) = {A ⊂ X : A ≠ ∅} is such that ϕ is upper semicontinuous if and only if it is continuous when viewed as a singlevalued map ϕ: Y → (A(X), A(τ )). In this paper, we seek a result like this from a reverse viewpoint, namely, given a set X and a topology Γ on A(X), we consider a natural topology R(Γ) on X, constructed from Γ satisfying R(Γ) = τ if Γ = A(τ ), and we give necessary and sufficient conditions to the upper semicontinuity of a multivalued map ϕ: Y ⊸ (X, R(Γ)) to be equivalent to the continuity of the singlevalued map ϕ: Y → (A(X), Γ).

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

415-423

Source:

Mathematica bohemica | 2013 Volume:138 | Number:4

Harvested from:

CDK

Metadata only:

false