Geodesic
Are initially $ω_1$ -compact separable regular spaces compact?
Fundamenta Mathematicae, Tome 154 (1997) no. 2, pp. 123-132

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DOI

We investigate the question of the title. While it is immediate that CH yields a positive answer we discover that the situation under the negation of CH holds some surprises. 
Alan Dow; Istvan  Juhász. Are initially $ω_1$ -compact separable regular spaces compact?. Fundamenta Mathematicae, Tome 154 (1997) no. 2, pp. 123-132. doi: 10.4064/fm-154-2-123-132
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     title = {Are initially $\ensuremath{\omega}_1$ -compact separable regular spaces compact?},
     journal = {Fundamenta Mathematicae},
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     year = {1997},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-154-2-123-132/}
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