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I need help in order to fully understand Example 3.2(d) ... ..

Example 3.2(d) reads as follows:

and Example 2.7(e) reads as follows:

In Example 3.2(d) we read the following:

" ... It is pseudometrizable since it is the topology generated by the trivial pseudometric on X, by part (e) of Example 2.7. ... ... "

I am somewhat lost by this example ...

Can someone please demonstrate that (X, \(\displaystyle \tau\) ) is the topology generated by the trivial pseudometric on X ... and explain the relation to part (e) of Example 2.7. ...

Help will be much appreciated ...

Peter