Abstract: To study some equivalent conditions of a Baire space and a Volterra space under Hausdorff separation axiom,using the general topology methods,some properties of the sequential closure of a subset of a space were studied,two conclusions about sequential closure and countable G_δ-set were gotten. By these conclusions,the regular condition which appeared in some equivalent conditions of a Baire space and a Volterra space can be replaced by Hausdorff separation axiom.