Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections

@article{Deutsch1983ContinuousSA,
  title={Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections},
  author={Frank Deutsch and Petar S. Kenderov},
  journal={Siam Journal on Mathematical Analysis},
  year={1983},
  volume={14},
  pages={185-194}
}
Two new continuity properties for set-valued mappings are defined which are weaker than lower semicontinuity. One of these properties characterizes when approximate selections exist. A few selection theorems characterized by the other property are established. Some applications are made to set-valued metric projections. 
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