In this article, we study the lattice of Lawvere-Tierney topologies on Hyland’s effective topos. For purpose, introduce a new computability-theoretic reducibility notion, which is common extension notions Turing and generalized Weihrauch reducibility. Based work by Lee van Oosten [Ann. Pure Appl. Logic 164 (2013), pp. 866-883], utilize notion for providing concrete description As an application...