2024/03/22 by Mauricio Chacón-Tirado, Chacón-Tirado, Mauricio, César Piceno +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Digital Image Processing Techniques #FOS: Mathematics #General Topology (math.GN) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2403.15595
openalex publication_date 2024/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the literature, various types of points and meager sets whose complements are connected have been studied, such as colocally connected points, non-weak cut points/sets, non-block points/sets, shore points/sets, etc. We extend that study, in the following way: considering a continuum X and a natural number n, we investigate sets A ∈ 2X meeting the criterion that X - A has at most n components, and we introduce degrees of connectivity of the complement of A. When n=1 and A is meager or singleton, these new definitions are equivalent to the known definitions of non-cut points/sets.