MAJOR RETRACTION IN UNIFORMITY DEFINING PROPOSITION.

This commit is contained in:
Bokuan Li
2026-06-21 21:56:28 -04:00
parent a57686be8f
commit f107df48bf
8 changed files with 97 additions and 11 deletions

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@@ -77,7 +77,7 @@ The axioms of uniform spaces strongly resembles working in a metric space. In fa
\]
\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.
\item[(UB2)] For each $J \subset I$ finite and $r > 0$,
\item[(UB3)] For each $J \subset I$ finite and $r > 0$,
\begin{align*}
\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) \\
&\subset \bigcap_{j \in J}E(d_j, r)