I was going through a proof and one of the statements said "observe that the characteristic functions are not continuous on $C[0,4]$" where $$C[0,4]= \{f: [0,4] \rightarrow \mathbb R: f\text{ is continuous}\}$$
Could someone explain why that is?
2026-04-01 15:12:19.1775056339
Why are characteristic functions are not continuous on set C[0,4]?
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