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Compacta with the shape finite complexes

Ross Geoghegan, R. Lacher (1976)

Fundamenta Mathematicae

Compactly generated shape theories

Thomas Sanders (1976)

Fundamenta Mathematicae

Convergence in compacta and linear Lindelöfness

Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (1998)

Commentationes Mathematicae Universitatis Carolinae

Let $X$ be a compact Hausdorff space with a point $x$ such that $X ∖ {x}$ is linearly Lindelöf. Is then $X$ first countable at $x$ ? What if this is true for every $x$ in $X$ ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when $X$ is, in addition, $ω$ -monolithic. We also prove that if $X$ is compact, Hausdorff, and $X ∖ {x}$ is strongly discretely Lindelöf, for every $x$ in $X$ , then $X$ is first countable. An example of linearly Lindelöf...

Countably compact spaces all countable subsets of which are scattered

István Juhász, Jan van Mill (1981)