In questo lavoro si studiano alcune proprieta dello spazio $(\mathcal{P}, H_\rho)$ delle mappe parziali con dominio chiuso, munito della topologia della metrica di Hausdorff. Si prova un'equivalenza tra le definizioni di buona posizione secondo Tykhonov e Hadamard di problemi di minimizzazione continui e vincolati, dove la dipendenza continua è descritta dalla metrica di Hausdorff sulle mappe parziali. Lo studio della completezza della metrica di Hausdorff nello spazio delle multifunzioni usco con dominio variabile permette di individuare condizioni per la completa metrizzabilità di $(\mathcal{P}, H_\rho)$
Referenze Bibliografiche
[1] A. ABD-ALLAH, Partial maps in algebra and topology, Ph. D. thesis, University of Wales (1979).
[2]
A. ABD-ALLAH -
R. BROWN,
A compact-open topology on partial maps with open domains,
J. London Math. Soc.,
21 (
1980), 480-486. |
Zbl 0436.54012[3]
M. ATSUJI,
Uniform continuity of continuous functions on metric spaces,
Pacific J. Math.,
8 (
1958), 11-16. |
Zbl 0082.16207[4]
K. BACK,
Concepts of similarity for utility functions,
J. Math. Econ.,
15 (
1986), 129-142. |
Zbl 0606.90014[5]
P. I. BOOTH -
R. BROWN,
Spaces of partial maps, fibred mapping spaces and the compact-open topology,
Topology Appl.,
8 (
1978), 181-195. |
Zbl 0373.54012[6]
G. BEER,
Topologies on Closed and Closed Convex Sets,
Kluwer (
1993). |
Zbl 0792.54008[7]
G. BEER,
Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance,
Proc. Amer. Math. Soc.,
95 (
1985), 653-658. |
Zbl 0594.54007[8]
G. BEER -
A. DI CONCILIO,
A generalization of boundedly compact metric spaces,
Comment. Math. Univ. Carolinae,
32, 2 (
1991), 361-367. |
fulltext EuDML |
Zbl 0766.54028[9]
P. BRANDI -
R. CEPPITELLI,
Existence, uniqueness and continuous dependence for hereditary differential equations,
J. Diff. Equations,
81 (
1989), 317-339. |
Zbl 0709.34062[10]
P. BRANDI -
R. CEPPITELLI,
A new graph topology.
Connections with compact open topology,
Appl. Analysis,
53 (
1994), 185-196. |
Zbl 0836.54010[11]
P. BRANDI -
R. CEPPITELLI,
A hypertopology intended for functional differential equations,
Appl. Analysis,
67 (
1997), 73-88. |
Zbl 0886.54009[12]
P. BRANDI -
R. CEPPITELLI -
Ľ. HOLÀ,
Topological properties of a new graph topology,
J. of Convex Analysis,
6, N. 1 (
1999), 29-40. |
fulltext EuDML |
Zbl 1122.54303[13]
P. BRANDI -
R. CEPPITELLI -
Ľ. HOLÀ,
Kuratowski convergence on compacta and Hausdorff metric convergence on compacta,
Comment. Math. Univ. Carolinae,
40, 2 (
1999), 309-318. |
fulltext EuDML |
Zbl 0976.54010[14] P. BRANDI - R. CEPPITELLI - Ľ. HOLÀ, Boundedly UC spaces, Hypertopologies and well-posedness, Rapporto tecnico N. 13, Department of Mathematics and Informatics, University of Perugia (2001).
[15]
R. CEPPITELLI -
L. FAINA,
Differential equations with hereditary structure induced by a Volterra type property,
Field Institute Communications,
29 (
2001), 73-91. |
Zbl 0988.34049[16]
J. P. R. CHRISTENSEN,
Theorems of Namioka and R.E. Johnson type for upper semicontinuous and compact valued set-valued mappings,
Proc. Amer. Math. Soc.,
86 (
1982), 649-655. |
Zbl 0506.54016[18] A. DI CONCILIO - S. A. NAIMPALLY, Function space topologies on (partial) maps, Recent progress in function spaces, Quaderni di Matematica (G. DI MAIO and Ľ. HOLÀ eds.), 3 (1999).
[19] R. ENGELKING, General Topology, Polish Scientific Publishers, Warszaw, (1977).
[20]
V. V. FILIPPOV,
Basic topological structures of the theory of ordinary differential equations,
Topology in Nonlinear Analysis,
Banach Centrum Publications,
35 (
1996), 171-192. |
fulltext EuDML |
Zbl 0847.34009[21]
Ľ. HOLÀ,
Hausdorff metric on the space of upper semicontinuous multifunctions,
Rocky Mountain Journal of Mathematics,
22 (
1992), 601-610. |
Zbl 0795.54029[22]
Ľ. HOLÀ,
Complete metrizability of generalized compact-open topology,
Topology and its Applications,
91(
1999), 159-167. |
Zbl 0987.54032[23]
Ľ. HOLÀ -
D. HOLY,
Further characterizations of boundedly UC spaces,
Comment. Math. Univ. Carolinae,
34, 1 (
1993), 175-183. |
fulltext EuDML |
Zbl 0828.54016[24]
Ľ. HOLÀ -
L. ZSILINSZKY,
Completeness properties of the generalized compact-open topology on partial functions with closed domains,
Topology Appl.,
110 (
2001), 303-321. |
Zbl 0974.54008[25]
Ľ. HOLÀ -
L. ZSILINSZKY,
Completeness properties of the Vietoris topology on partial functions with compact domains, preprint. |
Zbl 0974.54008[26] J. L. KELLEY, General Topology, Van Nostrand Reinhold Company, (1955).
[27]
H. P. KUNZI -
L. B. SHAPIRO,
On simultaneous extension of continuous partial functions,
Proc. Amer. Math. Soc.,
125 (
1997), 1853-1859. |
Zbl 0863.54012[28]
K. KURATOWSKI,
Sur l'espace des fonctions partielles,
Ann. Mat. Pura Appl. 40 (
1955), 61-67. |
Zbl 0065.34303[29]
K. J. LANGEN,
Convergence of dynamic programming models,
Mathematics of Operations research,
6 (
1981), 493-512. |
Zbl 0496.90085[30]
N. LEVINE,
Remarks on uniform continuity in metric spaces,
Amer. Math. Monthly,
67 (
1979), 562-563. |
Zbl 0100.18602[31]
J. NAGATA,
On the uniform topology of bicompactifications,
J. Inst. Polytech. Osaka City University,
1 (
1950), 28-38. |
Zbl 0041.51601[32] P. J. NYIKOS - L. ZSILINSZKY, Strong α-favorability of the (generalized) compactopen topology, Atti Sem. Mat. Fis. Univ. Modena, to appear.
[33]
J. P. REVALSKI,
Various aspects of well-posedness of optimization problems, in
R. Lucchetti -
J.P. Revalski (eds), «
Recent developments in well-posed variational problems»,
Kluwer (
1995), 229-256. |
Zbl 0880.49012[34]
J. P. REVALSKI -
N. V. ZHIVKOV,
Well-posed constrained optimization problems in metric spaces,
J. Opt. Theory Appl.,
76 (
1993), 145-163. |
Zbl 0798.49031[35]
G. R. SELL,
On the Fundamental Theory of Ordinary Differential Equations,
J. differential Equations,
1 (
1965), 371-392. |
Zbl 0151.10602[36] A. N. TYKHONOV, On the stability of the functional optimization problems, USSR J. Comp. Math. Phys., 6 (1966), 631-634.
[37]
W. WATERHOUSE,
On UC spaces,
Amer. Math. Mountly,
72 (
1965), 634-635. |
Zbl 0136.19802[38]
S. K. ZAREMBA,
Sur certaines familles de courbes en relations avec la theorie des equations differentielles,
Rocznik Polskiego Tow. Matemat.,
15 (
1936), 83-105. |
Zbl 0017.39802
Con il contributo del Ministero per i Beni e le Attività Culturali