On algebraic systems

Abstract The objective of this paper is to propose a generalization of algebraic closure space, namely algebraic system, and discuss its related properties. Firstly, we prove that the category of S0-algebraic systems is an epireflective subcategory of the category of algebraic systems. Then we show that the Sierpinski algebraic system (2; S) is a Sierpinski object in the category of algebraic systems and is concurrently an injective object in the category of S0-algebraic systems. Finally, we also demonstrate that the opposite category of continuous lattices is a reflective subcategory of the category of algebraic systems.