1. Let (X, d_x) be a metric space with the discrete metric. Show that: a) Every function f: X ? ? is continuous. b) What are the functions f: ? ? X?
Added by Scott P.
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The discrete metric $d_x$ is defined as follows: \[ d_x(x, y) = \begin{cases} 0 & \text{if } x = y \\ 1 & \text{if } x \neq y \end{cases} \] Show more…
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