Ahmed Hameed oleiwi Al Haidari

This work is aimed to introduce new definitions of maps by using the concept of compactness; called countable compact maps, pseudo compact maps, weakly countable compact maps, and sequentially compact maps. Moreover, this motivates us to find new relations between these types of maps. Indeed, we study the preservation of Kelley space by these forms of compact maps.

This work is aimed to introduce new definitions of maps by using the concept of compactness; called countable compact maps, weakly countable compact maps, almost countably compact map, pseudo-compact maps, sequentially compact maps, feebly compact maps, semi-compact maps, q-compact maps, po-compact maps, and almost compact maps. Moreover, this motivates us to find new relations between these types of maps. Indeed, we study the preservation of Kelley space by these forms of compact maps. Some properties of certain forms of compact maps are studied in this chapter, where we are detected certain basic properties for these concepts and therefore the effect of a Kelley space by them. Moreover, the composition of the same parity and different parity of mappings are discussed.