Filtered piece as kernel Sample Clauses

Filtered piece as kernel. Suppose that s > 1. If z is a cocycle representing a cohomology class in Xxxxx, then clearly z(Gs´1) = 0. Con- versely, if z is a continuous cocycle such that z(Gs´1) = 0, then it follows ď K văs´1 K from the identity Gs´1 = Ş Gv that K ker(z) u văs´1 (GK — Gv ) is an open cover of GK. Compactness of GK then implies that there is a v0 c s — 1 such that Gv0 c ker(z). In other words, we have just proved that K p K p K p FilăsH1(G , F (χ)) = ker ´H1(G , F (χ)) —r—es→ H1(Gs´1, F (χ))¯ . ` ˘
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