ON DECOMPOSITION OF THE REAL LINE IN TERMS OF RATIO SETS.

An attempt has been made in this paper to decompose the real line R into two complementary sets whose ratio sets have empty interior. Another decomposition of the real line has been made into uncountable pairwise disjoint sets {Xα}_α<ωc, where ω_c is the smallest uncountable ordinal, i.e. ∪ X_α<ωc X_α = R and X_α ∩ X_β = Φ for all α < ω_c; β < ω_c such that ratio sets of X_α (α < ω_c) have non-empty interior. [ABSTRACT FROM AUTHOR]