A convenient category of topological partial groups

Abstract

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).

Keywords

• Partial group
• Partial group homomorphism
• Topological group
• Topological partial group
• k ̲ $\underline {k}$ -partial group