# zbMATH — the first resource for mathematics

Short proofs of two theorems in topology. (English) Zbl 0780.54023
Summary: We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. H. Wicke and J. M. Worrell jun., Proc. Am. Math. Soc. 55, 427-431 (1976; Zbl 0323.54013)] A $$T_ 1$$ weakly $$\delta\theta$$-refinable countably compact space is compact. (ii) [A. Ostaszewski, ibid 68, 339-343 (1978; Zbl 0392.54014)]. A compact Hausdorff space which is a countable union of metrizable spaces is sequential.

##### MSC:
 54D30 Compactness 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54D55 Sequential spaces
Full Text: