University of GuilanJournal of Algebra and Related Topics2345-39312220141201First non-abelian cohomology of topological groups II436166ENH. SahlehUniversity of GuilanH. E. KoshkoshiUniversity of GuilanJournal Article20140809In this paper we introduce a new definition of the first non-abelian cohomology of topological groups. We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-abelian cohomology of a topological group by the notion of a principle homogeneous space.https://jart.guilan.ac.ir/article_66_401debc98c625ef131a511bc9335c425.pdf