we show that there exists a homeomorphism f between X^* Fan-Gottesman compactification of T_3-topological space (X,τ) and the canonical extension (X ̵̂,(U(β) ) ̵̂ ) of the pre-uniform space (X,U(β)). Therefore we also showed that X^* Fan-Gottesman compactification T_3-topological space (X,τ) can be viewed as the completion of certain pre-uniform space (X,U(β)).