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up vote 1 down vote favorite Consider $X = mathcal{C}([−1,1])$ with the usual norm $|f|_{infty} = sup_{tin [−1,1]}|f(t)|.$ Define $$mathcal{A}_{+}={ f in X : f(t)=f(−t) space forall tin [−1,1]},$$ $$mathcal{A}_{−}={ f in X : f(t)=−f(−t) space forall t in [−1,1]}. $$ Is $mathcal{A}_{+} +mathcal{A}_{−} = {f +g : f in mathcal{A}_{+},g in mathcal{A}_{−}}$ meager? I know this set is dense by the Stone-Weierstrass Theorem. However, that doesn't really help. I also know that if the set is closed, then it is meager, but I have difficulties deciding whether it is closed or not. I know the exponential function is a limit of a sequence of a sum of even and odd functions, however one could define it to be that, in which case it doesn't help. Any hints on how to get going on this problem, and on whether the set $mathcal{A}_...

up vote 53 down vote favorite 14 I would like to know if there has been any work relating legal code to complexity. In particular, suppose we have the decision problem "Given this law book and this particular set of circumstances, is the defendant guilty?" What complexity class does it belong to? There are results that have proven that the card game Magic: the Gathering is both NP and Turing-complete so shouldn't similar results exist for legal code? complexity-theory np-complete decision-problem share | cite | improve this question edited Nov 28 at 17:01 Juho 15.1k 5 40 89 ...