Cluster sets and topology
Jacek Marek Jędrzejewski, Stanisław Kowalczyk · Mathematica Slovaca · 2018
Abstract Limit numbers (cluster sets) of a real function of a real variable were discussed in the literature by many authors. Generalizations of cluster sets were considered by distinctions of some classes of sets which generated some kind of limit. In general they were close to some topology on the set of real numbers. However not all such classes allowed to define a topology on ℝ in a simple way. We consider some topologies in ℝ generated by those classes of sets. We investigate a connection between limit numbers generated by those classes and limit numbers defined by a topology generated by a class 𝔅.