Abstract
Paracompactness is a tool for splitting of a space. In this paper, new types of maps initiated called a paracompact map, S-paracompact mapping and β-paracompact mapping. The properties of these maps investigated. In addition, the relationships between a paracompact map with other maps discussed, such as Bourbaki proper mapping and closed mapping. Moreover, we studied the necessary conditions and properties for satisfying the composition of the new maps with the projection map and constant map are paracompact. The product of two paracompact maps also verified under necessary conditions
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