On the Existence of Continuous Selections in Subset Spaces with Ochan-Type Topologies

Abstract

We prove the existence of a continuous selection in the space $$\mathbb{P}$$ (X) (the nonempty subsets of a topologic space X) equipped with the Ochan-type $$(c_0 ,c_1 )$$ -topology in the case where X can be imbedded into the Tikhonov product of a countable family of left spaces (Theorem 1). We also prove the existence of a continuous selection on the exponent of a complete metric space in the Ochan-type $$(c_0 ,c_1 )$$ -topology (Theorem 2).