2
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I usually write the following:

$$\{m| m:A\to B\}$$

Is there a more succint notation?

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4
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The standard notation is $B^A$.

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  • $\begingroup$ Thank you. Does this notation have a name? $\endgroup$ – user56834 Apr 29 '18 at 6:49
  • $\begingroup$ Wikipedia doesn't list any name. $\endgroup$ – Yuval Filmus Apr 29 '18 at 6:52
  • $\begingroup$ @Programmer2134 Although I can't find a name, this notation seems to be derived from cardinal exponentiation and is related to the common notation of $2^B$ for the powerset of $B$. So, if you want to give a name for the notation, something like "function exponentiation notation" or "powerfunction notation" might work. Then again, a lot of notation is generally unnamed and this isn't seen as a problem. $\endgroup$ – Discrete lizard Apr 29 '18 at 9:36
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$A \to B$ is a common notation for the set of functions. For instance

$$ \begin{array}{l} f : (A\to B)\times A \to B \\ f(g,x) = g(x) \end{array} $$

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