On space of open quotient maps of a convergent sequence

Abstract

We consider the space of the classes of equivalences of continuous open maps defined on a convergent sequence induced by the Hausdorff metric. We show that $ \Psi (S) $ is a perfect zero-dimensional noncompact metric space which can be decomposed into the union of two sets, one of which is dense and the other is homeomorphic to the set of irrational numbers.