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B5

Part of 1970 Putnam

Problems(1)

Putnam 1970 B5

Source: Putnam 1970

5/17/2022
Let unu_n denote the ramp function un(x)={−n    for    x≤−n,  x      for    −n≤x≤n,  n      for    n≤x, u_n (x) =\begin{cases} -n \;\; \text{for} \;\; x \leq -n, \\ \; x \;\;\; \text{for} \;\; -n \leq x \leq n,\\ \;n \;\; \; \text{for} \;\; n \leq x, \end{cases} and let ff be a real function of a real variable. Show that ff is continuous if and only if un∘fu_n \circ f is continuous for all n.n.
Putnamfunctioncontinuity