关于Béla Bollobás的一个错误证明(英文)

ON A WRONG PROOF OF BLA BOLLOB■S

设N为自然数集。2~N表示N的全体子集构成的集,我们给予2~N以乘积拓扑。F.Galvin和K.Prikry为证明一个重要定理,给出一个重要的引理,但他们省略了引理证明的细节。Béla Bollobás给出引理的一个错误证明。本文中,我们给出错误证明的一个反例,并重新证明了前述引理。

Let N be the set of natural numbers. 2N denotes the set of subsets of N. We give 2N the product topology. On purpose to prove a theorem, F. Galvin and K. Prikry gave an important lemma, but they omitted the details of the lemma. Bela Bollobas gave a wrong proof of the lemma. In this paper, we gave a counterexample to the wrong proof and proved the lemma.