Previous |  Up |  Next

Article

Keywords:
upper semicontinuity; multifunction; closed graph; $c$-upper semicontinuity; complete uniform space
Summary:
The set of points of upper semicontinuity of multi-valued mappings with a closed graph is studied. A topology on the space of multi-valued mappings with a closed graph is introduced.
References:
[1] G. Beer: Topologies on closed and convex sets. Kluwer Academic Publishers, 1993. MR 1269778
[2] V. Baláž, Ľ. Holá, T. Neubrunn: Remarks on $c$-continuous. Acta Mathematica Univ. Com. L-LI (1987), 51–59.
[3] S. Dolecki: Semicontinuity in constrained optimization II. Control Cybernet. 2 (1978), 5–16. MR 0641777
[4] S. Dolecki, A. Lechicki: On structure of upper semicontinuity. J. Math. Anal. Appl. 88 (1982), 547–554. DOI 10.1016/0022-247X(82)90213-X | MR 0667078
[5] R. Engelking: General Topology. PWN, Warszaw, 1977. MR 0500780 | Zbl 0373.54002
[6] Z. Frolík: Generalizations of the $G_\delta $-property of complete metric spaces. Czechoslovak Math. J. 85 (1960). MR 0116305
[7] Ľ. Holá: An extension theorem for continuous functions. Czechoslovak Math. J. 113 (1988), 398–403. MR 0950293
[8] Ľ. Holá, I. Kupka: Closed graph and open mapping theorems for linear relations. Acta Mathematica Univ. Com. 46–47 (1985), 157–162. MR 0872338
[9] I. Kupka, V. Toma: Measure of noncompactness in topological spaces and upper semicontinuity of multifunctions. Rev. Roumaine Math. Pures Appl. 40 (1995), 455–461. MR 1404628
[10] A. Lechicki, S. Levi: Extension of semicontinuous multifunctions. Forum Math. (1990), 341–360. MR 1057877
[11] K. Sakálová: Continuity properties of multifunctions. Acta Mathematica Univ. Com. 56–57 (1989), 159–165. MR 1083019
Partner of
EuDML logo