2018/06/16 by Junguk Lee, Lee, Junguk, Michael P. Cohen +4
Mathematics · #03C45 #20E08 #28E15 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1806.06206
openalex publication_date 2018/06/16 · openalex created_date 2022/10/07 · openalex updated_date 2026/08/04
We introduce a notion of μ-structures which are certain locally compact group actions and prove some counterparts of results on Polish structures(introduced by Krupinski in \citeKru5). Using the Haar measure of locally compact groups, we introduce an independence, called μ-independence, in μ-structures having good properties. With this independence notion, we develop geometric stability theory for μ-structures. Then we see some structural theorems for compact groups which are μ-structure. We also give examples of profinite structures where μ-independence is different from nm-independence introduced by Krupinski for Polish structures.