Abstract
A topological space X is called maximally resolvable if it admits a largest possible family of pairwise disjoint, “maximally dense” subsets. More precisely, if Δ(X) denotes the least among the cardinal numbers of the nonvoid open subsets of X, then X is maximally resolvable if it has isolated points or there exists a family {Rα}α < Δ(X) of subsets of X, called a maximal resolution for X, such that ∪{Rα | α < Δ(X)} = X, Rγ ∩ Rδ==ϕ if γ ≠ δ, and, for each a and each nonvoid open subset V of X, the cardinality of Rα ∩ V is not less than Δ(X).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
