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10 June 2024
| N 12:19 | Open Balls form Local Basis of Metric Space diffhist +898 Caliburn talk contribs (Created page with "== Theorem == <onlyinclude> Let $\struct {M, d}$ be a metric space. Let $\tau$ be the topology on $M$ induced by $d$. Let $x \in X$. For each $\epsilon > 0$, let $\map {B_\epsilon} x$ be the open $\epsilon$-ball around $x$. Let $\BB_x = \set {\map {B_\epsilon} x : \epsilon > 0}$. Then $\BB_x$ is a local basis at $x$. </onlyinclude> == Proof...") | ||||