## M. Ismail, A. Szymanski

*Short proofs of two theorems in topology *

Comment.Math.Univ.Carolinae 34,3 (1993) 539-541. **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

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