2014/09/25 by Ігор Протасов, Protasov, Igor, Sergii Slobodianiuk +1 · 1 citation
Computer Science · Mathematics · #20F69 #22A15 #54D35 #Advanced Topology and Set Theory #Digital Image Processing Techniques #FOS: Mathematics #Group Theory (math.GR) #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1409.7350
openalex publication_date 2014/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a group and let X be a transitive G-space. We classify the subsets of X with respect to a translation invariant ideal J in the Boolean algebra of all subsets of X, introduce and apply the relative combinatorical derivations of subsets of X. Using the standard action of G on the Stone-\checkCech compactification βX of the discrete space X, we characterize the points p∈βX isolated in Gp and describe a size of a subset of X in terms of its ultracompanions in βX. We introduce and characterize scattered and sparse subsets of X from different points of view.