2024/04/09 by Tom Richmond, Richmond, Tom, Eliza Wajch +1
Decision Sciences · #03E35 #06A75 #06F30 #54A05 #54A10 #54A35 #54F05 #54F30 #54G12 #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2404.06623
openalex publication_date 2024/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A (generalized) topological space is called an iso-dense space if the set of all its isolated points is dense in the space. The main aim of the article is to show in ZF a new characterization of iso-dense spaces in terms of special quasiorders. For a non-empty family A of subsets of a set X, a quasiorder \lesssimA on X determined by A is defined. Necessary and sufficient conditions for A are given to have the property that the topology consisting of all \lesssimA-increasing sets coincides with the generalized topology on X consisting of the empty set and all supersets of non-empty members of A. The results obtained, applied to the quasiorder \lesssimD determined by the family D of all dense sets of a given (generalized) topological space, lead to a new characterization of non-trivial iso-dense spaces. Independence results concerning resolvable spaces are also obtained.