Abstract
We investigate the following weak Ramsey property of a cardinal.: If. is coloring of nodes of the tree kappa( partial derivative is regular, then kappa (sic) (kappa)(omega)(<omega) and that b (sic) ( b)(omega)(<omega) and partial derivative (sic) (partial derivative)(omega)(<omega). The arrow is applied to prove a generalization of a theorem of Hurewicz: A C. ech- analytic space is s- locally compact iff it does not contain a closed homeomorphic copy of irrationals.