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- W4302386217 abstract "Let $G$, $R$ and $A$ be topological groups. Suppose that $G$ and $R$ act continuously on $A$, and $G$ acts continuously on $R$. In this paper, we define a partially crossed topological $G-R$-bimodule $(A,mu)$, where $mu:Arightarrow R$ is a continuous homomorphism. Let $Der_{c}(G,(A,mu))$ be the set of all $(alpha,r)$ such that $alpha:Grightarrow A$ is a continuous crossed homomorphism and $mualpha(g)=r^{g}r^{-1}$. We introduce a topology on $Der_{c}(G,(A,mu))$. We show that $Der_{c}(G,(A,mu))$ is a topological group, wherever $G$ and $R$ are locally compact. We define the first cohomology, $H^{1}(G,(A,mu))$, of $G$ with coefficients in $(A,mu)$ as a quotient space of $Der_{c}(G,(A,mu))$. Also, we state conditions under which $H^{1}(G,(A,mu))$ is a topological group. Finally, we show that under what conditions $H^{1}(G,(A,mu))$ is one of the following: $k$-space, discrete, locally compact and compact." @default.
- W4302386217 created "2022-10-06" @default.
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- W4302386217 date "2014-02-17" @default.
- W4302386217 modified "2023-09-25" @default.
- W4302386217 title "On Topological Structure of the First Non-abelian Cohomology of Topological Groups" @default.
- W4302386217 doi "https://doi.org/10.48550/arxiv.1402.4168" @default.
- W4302386217 hasPublicationYear "2014" @default.
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