Definition -- what is a partial metric space?
A partial metric space
[Mat92, Mat94] is a pair
(X, p:S×S->R+)
(where R+
denotes the set of all non negative real numbers) such that
- p(x,y) = p(y,x)
(symmetry)
- If p(x,x) = p(x,y) = p(y,y) then x=y
(equality)
- p(x,x) <= p(x,y)
(small self-distances)
- p(x,z) + p(y,y) <=
p(x,y) + p(y,z)
(triangularity)
A partial metric space is a generalisation of the notion
of metric space [Su75]
such that distances of the form p(x,x)
are no longer necessarily zero.
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