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Short proofs of two theorems in topology

Mohammad Ismail;  Andrzej Szymański — 1993

Commentationes Mathematicae Universitatis Carolinae

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 δ θ -refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.

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