Extension of scmapping on Duplicate of Space

In 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 space, so-set, so-paracompact space, S-paracompact space, sc-mapping, quasi-continuous mapping