Färbungen großer Würfel mit bunten Wegen (Q795038)

In 1976 V. Rödl and J. Nešetřil asked whether there exists a cardinal number k such that for every mapping \(f:\prod_{k}I\to \{0,1\}\) there exists an embedding e of the real unit interval I into \(I^ k\) such that \(f\circ e\) is constant. The question was answered by \textit{W. Weiss} [Topology, Vol. II, 4th Colloq. Budapest 1978, Colloq. Math. Soc. János Bolyai 23, 1249-1255 (1980; Zbl 0434.54011)] and independently by the author [Habilitationsschrift (1981)]. The paper contains a proof of Theorem 1: Let k be a cardinal in \([\omega,(2^{\omega})^{(+\omega)}]\) and T a \(T_ 2\)-space of power k; then there is a mapping \(f:T\to 2^{\omega}\) such that for every embedding \(e: L\to T\) one has \((f\circ e)''I=2^{\omega}.\) The author formulates a principle \(*_ k\) and proves that for every \(k>0\) one has \(Con(ZFC)\Rightarrow Con(ZFC+CH+*_ k+\neg GCH)\) (Theorem 3).