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Let $A$ be an abelian topological $G$-module. We give an interpretion for thesecond cohomology, $H^{2}(G,A)$, of $G$ with coefficients in $A$. As a resultwe show that if $P$ is a projective topological group, then $H^{2}(P,A)=0$ forevery abelian topological $P$-module $A$.

Standard Projective Simplicial Kernels and the Second Abelian Cohomology of Topological Groups