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Date: 27-5-2021
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Date: 13-6-2021
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Date: 7-8-2021
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A topology on a set whose open sets are the unions of open balls
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where is a pseudometric on
,
is any point of
, and
.
There is a remarkable difference between a metric and a pseudometric topology. The former is always , whereas the latter is, in general, not even
. In fact, a pseudometric allows
for some distinct points
and
, and then every open ball containing
contains
and conversely, so that no open set can separate the two points.
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