>**Problem.** Is the separability of the Gelfand space of a semi-simple commutative Banach algebra $A$ equivalent to the existence of a countable family $\{\varphi_n\}_{n\in\omega}$ of multiplicative linear functionals on $A$ such that for each $a\in A$ its spectrum coincides with the closure of the union $\bigcup_{n\in\omega}\varphi_n(a)$?

(The problem was posed 09.08.2015 by Michal Wojciechowski on [page 14][1] of [Volume 0][2] of the [Lviv Scottish Book][3]).

The prize for solution: *A dinner in "Szkocka"*. 


  [1]: http://www.math.lviv.ua/szkocka/viewpage.php?vol=0&page=14
  [2]: http://www.math.lviv.ua/szkocka/viewbook.php?vol=0
  [3]: http://www.math.lviv.ua/szkocka