Our basic references for quasi-metric spaces are [1, 2] and for asymmetric normed space it is [3].A quasi-pseudometric on a set is a function such that for all (i) ; (ii) .If satisfies conditions (i) and (ii) above but we allow , then is said to be an extended quasi-pseudometric on .Following the modern terminology, a quasi-pseudometric on satisfying () if and only if is called a quasi-metric on .