Geodesic
Singularities and equicontinuity of certain families of set-valued mappings
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 353-365

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In the present paper we establish an abstract principle of condensation of singularities for families consisting of set-valued mappings. By using it as a basic tool, the condensation of the singularities and the equicontinuity of certain families of generalized convex set-valued mappings are studied. In particular, a principle of condensation of the singularities of families of closed convex processes is derived. This principle immediately yields the uniform boundedness theorem stated in [1, Theorem 2.3.1].
In the present paper we establish an abstract principle of condensation of singularities for families consisting of set-valued mappings. By using it as a basic tool, the condensation of the singularities and the equicontinuity of certain families of generalized convex set-valued mappings are studied. In particular, a principle of condensation of the singularities of families of closed convex processes is derived. This principle immediately yields the uniform boundedness theorem stated in [1, Theorem 2.3.1].
Classification : 26B25, 46N10, 54C60
Keywords: condensation of the singularities; equicontinuity; generalized convex set-valued mappings; closed convex processes 
Trif, Tiberiu. Singularities and equicontinuity of certain families of set-valued mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 353-365. http://geodesic.mathdoc.fr/item/CMUC_1998_39_2_a11/
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     author = {Trif, Tiberiu},
     title = {Singularities and equicontinuity of certain families of set-valued mappings},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {353--365},
     year = {1998},
     volume = {39},
     number = {2},
     mrnumber = {1651971},
     zbl = {0937.46064},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998_39_2_a11/}
}
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