Small diagonals and cardinal invariants.

The notion of a κ -splitting diagonal was introduced and studied by Tkachuk. In this paper, we prove that there exists a locally countable, locally compact space with an ω 1 -splitting diagonal but no G δ -diagonal. Using the Erdös-Radó's theorem, we also prove that every DCCC homogeneous space X with a regular G δ -diagonal such that π χ (X) = ω has cardinality at most c. Some new questions are also posed. [ABSTRACT FROM AUTHOR]