I need a proof for this proposition:

If a uniformity $U$ on $X$ has a countable fundamental system of entourages, then it can be defined by a pseudometric on $X$.

which is the proposition 2 on page 142 of this book. I can't see the proof page.

even a sketch of proof is welcome. thanks.

I need a proof for this proposition:

If a uniformity $\mathfrak U$ on $X$ has a countable fundamental system of entourages, then it can be defined by a pseudometric on $X$.

which is the proposition 2 on page 142 of this book. I can't see the proof page.

even a sketch of proof is welcome. thanks.

I need a proof for this proposition:

If a uniformity $U$ on $X$ has a countable fundamental system of entourages, then it can be defined by a pseudometric on $X$.

which is the proposition 2 on page 142 of this book. I can't see the proof page.

even a sketch of proof is a welcome. thanks.

I need a proof for this proposition:

If a uniformity $U$ on $X$ has a countable fundamental system of entourages, then it can be defined by a pseudometric on $X$.

which is the proposition 2 on page 142 of this book. I can't see the proof page.

even a sketch of proof is welcome. thanks.