Abstract:We present short and elementary proofs of the following two known theorems in General Topology: \item "(i)" [H. Wicke and J. Worrell] A $T_1$ weakly $\delta \theta $-refinable countably compact space is compact. \item "(ii)" [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.
Keywords: countably compact, initially $\kappa $-compact, weakly $\delta \theta $-refinable, $\kappa $-refinable, sequential
AMS Subject Classification: 54D30, 54D20, 54D55