2017/03/02 by Ігор Протасов, Igor Protasov, Protasov, Igor +2
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #General Topology (math.GN) #math.GN
paper · pdf · doi:10.48550/arxiv.1703.00695
$G$-space, recurrent subset, ultrafilters, Stone-$\check{C}$ech compactification
arxiv created 2017/03/02 · openalex publication_date 2017/03/02 · arxiv updated 2017/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and analyze the following general concept of recurrence. Let G be a group and let X be a G-space with the action G× X\longrightarrow X, (g,x)\longmapsto gx. For a family \mathfrakF of subset of X and A∈ \mathfrakF, we denote Δ_\mathfrakF(A)=\g∈ G: gB⊆ A for some B∈ \mathfrakF, B⊆ A\, and say that a subset R of G is \mathfrakF-recurrent if R\bigcap Δ_\mathfrakF (A)≠∅ for each A∈ \mathfrakF.