Metric spaces and enriched categories 2
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Lawvere generalized topological spaces, which arise as categories
enriched in the monoidal category |R| of nonnegative real numbers
with unit 0 and tensor +, are also known in the literature
as quasimetric spaces; see "All Topologies Come From Generalized Metrics"
Ralph Kopperman in The American Mathematical Monthly, Vol. 95, No. 2 (Feb., 1988), pp. 89-97
Kopperman shows that all topological spaces arise from quasimetric spaces, where the quasimetric has values in a "value semigroup."
flengyel 3 years ago