Abstract
In this work, the concept of the paracompact map has been generalized to other new types of maps, in addition to the fact that the paracompact map has been linked to these new maps. Accordingly, we will separate these new types of maps into two classes, the first class is called a strong form which implies a paracompact map under certain conditions. While the other class is called a weaker form of a paracompact map, whereas the paracompact map implies them. Finally, the composition operations of paracompact maps are studied.
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