Metrizability of a type of special cone metric spaces

In order to get the concept of convergence of sequence in the cone metric space with cone having no interiors and the metrizablity of this type of cone metric space,this paper defined convergence consequence,Cauchy sequence and completion by using the property of normal cone;further,defined a real metric induced by cone metric by norm of vector that controls the cone metric of cone metric space with cone having no interiors,then it is proved to be equivalent between convergence consequence,Cauchy sequence and complete defined by cone metric and convergence consequence,Cauchy sequence and complete defined by real metric induced by cone metric,and a type of metrizability for this type of cone metric space with cone having no interiors is derived.By using altering distance function,this study proved the theorem of a type of fixed point in the special type of cone metric space.