Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8226Research ArticleExtension of scmapping on Duplicate of SpaceKlyushinV LDepartement of Higher Mathematicsvklyushin@mail.ruJalal Hatem Hussein Al Bayati-Departement of Higher Mathematicsjalalintuch@yahoo.comPeoples’ Friendship University of Russia15032014351008092016Copyright © 2014,2014In this paper we consider topological duplications of so-paracompact spaces and extensions of sc-mappings on duplicate. The notions of so-paracompact space and sc-mapping (which generalize the notions of paracompact space and continuous mapping respectively) were introduced by the authors recently and based on so-sets (so-set is the union of the open set and the nowhere dense set). The aim of the work is the investigation of the properties of duplicates of mentioned spaces and mappings. It is proved that Alexandroff duplicate of soparacompact space is so-paracompact. It is proved also that mentioned duplicate is almost paracompact space. It was established that natural extension of sc-mapping on duplicate of space is so-mapping which possess of supplementary properties. It is proved that the natural extension of quasi-continuous mapping is quasi-continuous.topological duplicate of spaceso-setso-paracompact spaceS-paracompact spacesc-mappingquasi-continuous mappingтопологическое удвоение пространстваso-множествоso-паракомпактное пространствоS-паракомпактное пространствоsc-отображениеквазинепрерывное отображение