| Summary: | Abstract In this paper, the concept of ℘-continuous map is introduced and some of their basic properties are discussed. Also, the category Ḱ $\mathbf {K}\acute {}$, of topological partial groups, as objects and the ℘-morphisms of topological partial groups, as arrows, is introduced, which is alternative to the category K, of topological spaces, as objects and k-continuous maps, as arrows, and satisfies the same nice properties of the category k p g, of k̲ $\underline {k}$-partial groups, as objects, and the morphisms of k̲ $\underline {k}$-partial groups, as arrows (Abd- Allah et al., J. Egyption Math. Soc 25:276-278, 2017).
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