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Topology of metric spaces S. Kumaresan
Publisher: Alpha Science International, Ltd

Is it that a property is metric if it is related to the metric used on the space. Math in Plain English: Topology I – Metric Spaces I. That's how in the same space like R, we can prove that cauchiness is not topological by changing the metric. My quick question is this: I know it's true that any sequence in a compact metric space has a convergent subsequence (ie metric spaces are sequentially compact). The concept of convergence of sequences in a D-metric space was introduced by him. Some of his fixed point theorems were found to be incomplete or false by S.V.R. Try using the pythagorean distance formula to make this a metric space, or you could work out a subbase of the product topology. The notion of a D-metric space was originally introduced by Dhage. Given of distances between any two points, we've got a topology? So is Cauchiness a metric property? However, it would be too abstract to do topology on spaces with no distance, so I'll keep it simple here and restrict ourselves to metric topologies.