If \(\kappa > \aleph_0\) then \(\kappa \to(\kappa,\operatorname{Top}K_\kappa)^2\), i.e., every graph on \(\kappa\) vertices contains either an independent set of \(\kappa\) vertices, or a topological \(K_\kappa\), iff \(\kappa\) is regular and there is no \(\kappa\)-Suslin tree. Concerning the statement \(\omega_2\to(\operatorname{Top}K_{\omega_2})^2_\omega\), i.e., in every coloring of the edges of \(K_{\omega_2}\) with countably many colors, there is a monochromatic topological \(K_{\omega_2}\), both the statement and its negation are consistent with the Generalized Continuum Hypothesis.

如果\（\ kappa> \ aleph_0 \），则\（\ kappa \ to（\ kappa，\ operatorname {Top} K_ \ kappa）^ 2 \），即\（\ kappa \）顶点上的每个图都包含一个独立的\（\ kappa \）顶点集或拓扑\（K_ \ kappa \），如果iff \（\ kappa \）是常规的，则没有\（\ kappa \）- Suslin树。关于语句\（\ omega_2 \ to（\ operatorname {Top} K _ {\ omega_2}）^ 2_ \ omega \），即\（K _ {\ omega_2} \）的边缘的每种着色都有很多颜色，存在单色拓扑\（K _ {\ omega_2} \），该陈述及其否定词均与广义连续体假说一致。