MAJOR RETRACTION IN UNIFORMITY DEFINING PROPOSITION.
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@@ -77,7 +77,7 @@ The axioms of uniform spaces strongly resembles working in a metric space. In fa
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\item[(UB1)] For each $i \in I$, $d(x, x) = 0$ for all $x \in X$. Thus for any $i \in I$ and $r > 0$, $E(d_i, r)$ contains the diagonal.
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\item[(UB2)] For each $J \subset I$ finite and $r > 0$,
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\item[(UB3)] For each $J \subset I$ finite and $r > 0$,
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\begin{align*}
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\paren{\bigcap_{j \in J}E(d_j, r/2)} \circ \paren{\bigcap_{j \in J}E(d_j, r)} &\subset \bigcap_{j \in J}E(d_j, r/2) \circ E(d_j, r/2) \\
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&\subset \bigcap_{j \in J}E(d_j, r)
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