Sahleh, H. and Koshkoshi, H. E.
(2014)
*On Topological Structure of the First Non-abelian Cohomology of Topological Groups.*
British Journal of Mathematics & Computer Science, 4 (12).
pp. 1758-1770.
ISSN 22310851

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## 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 dene a partially crossed topological G - R-bimodule (A, μ), where μ: A→ R is a continuous homomorphism. Let Derc(G, (A, μ)) be the set of all (α, r) such that α : G → A is a continuous crossed homomorphism and μα(g) = rgr-1. We introduce a topology on Derc(G, (A, μ)). We show that Derc(G, (A, μ)) is a topological group, wherever G and R are locally compact. We define the first cohomology, H1(G, (A, μ)), of G with coecients in (A, μ)) as a quotient space of Derc(G, (A, μ)). Also, we state conditions under which H1(G, (A, μ)) is a topological group. Finally, we show that under what conditions H1(G, (A, μ)) is one of the following: k-space, discrete, locally compact and compact.

Item Type: | Article |
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Subjects: | Eurolib Press > Mathematical Science |

Depositing User: | Managing Editor |

Date Deposited: | 20 Jun 2023 07:09 |

Last Modified: | 20 Oct 2023 04:04 |

URI: | http://info.submit4journal.com/id/eprint/2147 |