Abstract:The authors give a ZFC example for a space with $\text {Split}\kern 0.8pt (\Omega , \Omega )$ but not $\text {Split}\kern 0.8pt (\Lambda , \Lambda )$.
Keywords: $\omega $-cover, $\lambda $-cover, $\text {Split}\kern 0.8pt(\Omega ,\Omega )$, $\text {Split}\kern 0.8pt(\Lambda ,\Lambda )$, ultrafilter
AMS Subject Classification: 04A20, 54D20