The authors give a ZFC example for a space with $\text{\it Split}\kern 0.8pt (\Omega , \Omega )$ but not $\text{\it Split}\kern 0.8pt (\Lambda , \Lambda )$.
@article{118936, author = {Winfried Just and Andreas Tanner}, title = {Splitting $\omega$-covers}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {38}, year = {1997}, pages = {375-378}, zbl = {0887.04001}, mrnumber = {1455505}, language = {en}, url = {http://dml.mathdoc.fr/item/118936} }
Just, Winfried; Tanner, Andreas. Splitting $\omega$-covers. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 375-378. http://gdmltest.u-ga.fr/item/118936/
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