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Results tagged with uniform-spaces
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user 2000
7
votes
Accepted
A uniformity with a countable base is a pseudometric uniformity.
First, find a fundamental system of entourages $U_0 \supseteq U_1 \supseteq \cdots$ such that
$U_0 = X \times X$
$(x_0,x_1) \in U_i$ iff $(x_1,x_0) \in U_i$.
If $(x_0,x_1),(x_1,x_2),(x_2,x_3) \in U_ …
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