This article is devoted to a transversal map continuity on a topological group G. For the topological group G its proper nontrivial subgroups $G_k$ are taken $G_k\subset G$, $G_k\ne G$. In G relative to $G_k$ the transversal set $V_{G,G_k}=V_k$ is considered. The coarsest topologies ${\mathcal{T}}_{G;G_k,V_k}$ on G are studied relative to which the transversal maps ${\tau }_{G_k}^G:G\to V_k$ are continuous and $(G,{\mathcal{T}}_{G;G_k,V_k})$ is the topological group. Then incomparable topologies on G are investigated with the help of transversal maps.

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论横向映射的连续性和拓扑群的不可比拓扑

本文致力于研究拓扑群G上的横向映射连续性。对于拓扑群G，它的真非平凡子群$G_{ķ}$被采取$G_{ķ}\subset G$,$G_{ķ}\ne G$. 在G相对于$G_{ķ}$横向集${五}_{G,G_{ķ}}={五}_{ķ}$被认为。最粗略的拓扑${\mathcal{吨}}_{G;G_{ķ},{五}_{ķ}}$在G上研究相对于其横向映射${\tau }_{G_{ķ}}^G：G\to {五}_{ķ}$是连续的并且$(G,{\mathcal{吨}}_{G;G_{ķ},{五}_{ķ}})$是拓扑群。然后借助横向映射研究G上无与伦比的拓扑。