On matrix points in Čech--Stone compactifications of discrete spaces

summary:We prove the existence of $(2^\tau, \tau )$-matrix points among uniform and regular points of Čech--Stone compactification of uncountable discrete spaces and discuss some properties of these points

Cardinal invariants and compactifications

summary:We prove that every compact space $X$ is a Čech-Stone compactification of a normal subspace of cardinality at most $d(X)^{t(X)}$, and some facts about cardinal invariants of compact spaces