C^*-metric spaces

‎The purpose of this article is to introduce the notion of an \mathfrak{A}-meter‎, ‎as an operator-valued distance mapping on a set X and investigating the theory of \mathfrak{A}-metric spaces‎, ‎where \mathfrak{A} is a noncommutative C^*-algebra‎. ‎We demonstrate that each metric space may be seen as an \mathfrak{A}-metric space and that every \mathfrak{A}-metric space (X,\delta) can be regarded as a topological space (X,\tau_{\delta})‎.

C^*-metric spaces Keywords:

‎C^*-algebra , C^*-metric space , allowance set , downward/upward directed set‎ , ‎positive elements‎