Automatic continuity and openness of convex relations

Borwein, J. M.

doi:10.1090/S0002-9939-1987-0866428-4

Automatic continuity and openness of convex relations
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Proc. Amer. Math. Soc. 99 (1987), 49-55 Request permission

Abstract:

We establish open mapping and lower semicontinuity results for convex relations which are generalizations of classical results on continuity of positive linear mappings. These results do not require closure of the relation. Several applications are given.

References

Convex relations in optimization and analysis

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