Graph convergence of set-valued maps and its relationship to other convergences

• Autorzy: Del Prete, I. , Di Iorio, M. , Holá, L.
• Języki publikacji: EN

Abstrakty

EN

The notion of even-outer-semicontinuity for set-valued maps is introduced and compared with related ones from [4] and [11]. The coincidence of these notions provides a new characterization of compactness and of local compactness. The following result is proved: Let X be a topological space, Y a uniform space, {Fσ : σ ∈ ∑} be a net of set-valued maps from X to Y and F be a set valued map from X to Y. Then any two of the following conditions imply the third: (1) the net {Fσ : σ ∈ ∑} is evenly-outer semicontinuous; (2) the net {{Fσ : σ ∈ ∑} is graph convergent to F; (3) the net {Fσ : σ ∈ ∑} is pointwise convergent to F. This theorem generalizes some results from [4] and [11].

Słowa kluczowe

PL

odwzorowanie wartości zadanej; wykres konwergencji; zbieżność; zbieżność w jednym punkcie; zbieżność punktowa; zbieżność ciągła

EN

set-valued map; graph convergence; pointwise convergence; continuous convergence; even-outer-semicontinuity

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2000
• Tom: Vol. 6, nr 2
• Strony: 213-226
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Del Prete, I.

autor

Di Iorio, M.

autor

Holá, L.

• Dipartimento Di Matematica e Applicazioni Universitá Degli Studi Di Napoli Via Claudio 21, 80125 Napoli, Italy,