Pseudometric Topology
المؤلف:
المرجع الالكتروني للمعلوماتيه
المصدر:
www.almerja.com
الجزء والصفحة:
...
15-8-2021
2977
Pseudometric Topology
A topology on a set 
whose open sets are the unions of open balls
![B(X_0,r)=<span style=]() {x in x|g(x_0,x)<r}, " src="https://mathworld.wolfram.com/images/equations/PseudometricTopology/NumberedEquation1.gif" style="height:18px; width:186px" /> |
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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