Geodesic
Short proofs of two theorems in topology
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 539-541

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We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A $T_1$ weakly $\delta \theta $-refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.
Classification : 54D20, 54D30, 54D55
Keywords: countably compact; initially $\kappa $-compact; weakly $\delta \theta $-refinable; $\kappa $-refinable; sequential 
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Ismail, M.; Szymański, A. Short proofs of two theorems in topology. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 539-541. http://geodesic.mathdoc.fr/item/CMUC_1993__34_3_a15/