any help is greatly appreciated as I really am unsure on where to start! I think it has something to do with Cauchy sequences but again I am very unsure on how to tackle this problem.
2026-04-06 04:40:38.1775450438
Show that if $E$ ⊆ $S$ and $F$ ⊆ $T$ then χE×F (s, t) = χE (s) · χF (t) for all (s, t) ∈ $S$ × $T$
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$$\chi_{E\times F}(s,t)=1\iff (s,t)\in E\times F\iff s\in E\text{ and }t\in F\iff \chi_E(s)\chi_F(t)=1.$$