Geodesic
$\aleph_0$-spaces and images of separable metric spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 62-67

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A space $X$ is an $\aleph_0$-space if and only if $X$ is a sequencecovering and compact-covering image of a separable metric space. It follows that a space $X$ is a $k$-and-$\aleph_0$-space if and only if $X$ is a sequencecovering and compact-covering, quotient image of a separable metric space. 
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     author = {Y. Ge},
     title = {$\aleph_0$-spaces and images of separable metric spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {62--67},
     publisher = {mathdoc},
     volume = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a3/}
}
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Y. Ge. $\aleph_0$-spaces and images of separable metric spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 62-67. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a3/