How can we define distance between two sets say, $A$ and $B$ in a partial metric space $(X, p)$? Will it be non-symmetric as in the case of a metric $d$, i.e.; we have $d(A, B)$ not equal to $d(B, A)$ in general. Will that be the case for the partial metric $p$?
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How do you define an open set in a partial non-symmetric metric space? say an open ball. I am kinda curious. – Shuhao Cao Jun 10 '13 at 16:14
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My question is for the case of a symmetric partial metric space – MINI Jun 10 '13 at 16:19
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Are you worried about the distance function possibly taking infinite values? Even in the case of regular metric spaces the Hausdorff distance does not always define a metric. – Dan Rust Jun 10 '13 at 16:39