Geodesic
On the theory of $K$-analytic spaces
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 76-82 
E. G. Pytkeev. On the theory of $K$-analytic spaces. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 76-82. http://geodesic.mathdoc.fr/item/TIMM_1998_5_a5/
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     author = {E. G. Pytkeev},
     title = {On the theory of $K$-analytic spaces},
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     pages = {76--82},
     year = {1998},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_1998_5_a5/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Main results are the following. Let $X$ be a regular $K$-analytic space. Then (1) $X$ is hereditarily Lindelöf and hereditarily separable if and only if there does not exist any strongly increasing transfinite sequence $\{f_{\alpha}\colon\alpha\omega_1\}$ of functions of the first Baire class; (2) every directed acontinuous covering of $X$ by $G_\delta$ sets lias a countable subcovering.