On the topology of D‐metric spaces and generation of D‐metric spaces from metric spaces
S. V. R. Naidu, K. P. R. Rao, N. Srinivasa Rao · International Journal of Mathematics and Mathematical Sciences · 2004
An example of a D‐metric space is given, in which D‐metric convergence does not define a topology and in which a convergent sequence can have infinitely many limits. Certain methods for constructing D‐metric spaces from a given metric space are developed and are used in constructing (1) an example of a D‐metric space in which D‐metric convergence defines a topology which is T1 but not Hausdorff, and (2) an example of a D‐metric space in which D‐metric convergence defines a metrizable topology but the D‐metric is not continuous even in a single variable.