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Graph Convergence of Set-Valued Maps and its Relationship to Other Convergences
| Content Provider | Scilit |
|---|---|
| Author | Prete, I. Del Iorio, M. Di Holá, L̆. |
| Copyright Year | 2000 |
| Abstract | The notion of even-outer-semicontinuity for set-valued maps is introduced and compared with related ones from [Bagh, Wets, Set-Valued Anal. 4: 333–360, 1996] and [Kowalczyk, Demonstratio Math. 27: 79–87, 1994]. 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 ∈ 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 ∈ Σ} is evenly-outer semicontinuous; (2) the net {Fσ : σ ∈ Σ} is graph convergent to F; (3) the net {Fσ : σ ∈ Σ} is pointwise convergent to F. This theorem generalizes some results from [Bagh, Wets, Set-Valued Anal. 4: 333–360, 1996] and [Kowalczyk, Demonstratio Math. 27: 79–87, 1994]. |
| Related Links | http://www.heldermann-verlag.de/jaa/jaa06/jaa06013.pdf |
| Ending Page | 226 |
| Page Count | 14 |
| Starting Page | 213 |
| ISSN | 14256908 |
| e-ISSN | 18696082 |
| DOI | 10.1515/jaa.2000.213 |
| Journal | Journal of Applied Analysis |
| Issue Number | 2 |
| Volume Number | 6 |
| Language | English |
| Publisher | Walter de Gruyter GmbH |
| Publisher Date | 2000-01-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of Applied Analysis Cybernetical Science Set-valued Map Graph Convergence Pointwise Convergence Continuous Convergence Even-outer-semicontinuity Journal: Journal of Applied Analysis, Vol- 6 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Mathematical Physics Computational Theory and Mathematics Statistics, Probability and Uncertainty |
