An extension of Kelley's closed relation theorem to relator spaces

Árpád Száz

In this paper we prove a straightforward extension of the dual of Kelley's famous closed relation theorem to a pair of relations on one relator (generalized uniform) space to another. In particular, we show that an almost uniformly lower semi-continuous closed relation on a topologically semisymmetric relator space to a complete metric type relator space is uniformly lower semicontinuous.