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Pseudometric space
In
mathematics
, a
pseudometric
or
semi-metric space
is a generalized
metric space
in which the distance between two distinct points can be zero. In the same way as every
normed space
is a
metric space
, every
seminormed space
is a pseudometric space. Because of this analogy the term
semimetric space
(which has a different meaning in
topology
) is sometimes used as a synonym, especially in
functional analysis
.
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