Geodesic
Spaces With $\sigma$-Locally Finite Lindelöf sn-Networks
Publications de l'Institut Mathématique, _N_S_93 (2013) no. 107, p. 145

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We prove that a space $X$ has a $\sigma$-locally finite Lindelöf sn-network if and only if $X$ is a compact-covering compact and mssc-image of a locally separable metric space, if and only if $X$ is a sequentially-quotient $\pi$ and mssc-image of a locally separable metric space, where ``compact-covering'' (or ``sequentially-quotient'') can not be replaced by ``sequence-covering''. As an application, we give a new characterization of spaces with locally countable weak bases.
Classification : 54E35 54E40 54D65 54E99
Keywords: weak base, sn-network, locally finite, Lindelöf, compact-covering map, compact map, mssc-map 
@article{PIM_2013_N_S_93_107_a11,
     author = {Luong Quoc Tuyen},
     title = {Spaces {With} $\sigma${-Locally} {Finite} {Lindel\"of} {sn-Networks}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {145 },
     publisher = {mathdoc},
     volume = {_N_S_93},
     number = {107},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2013_N_S_93_107_a11/}
}
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Luong Quoc Tuyen. Spaces With $\sigma$-Locally Finite Lindelöf sn-Networks. Publications de l'Institut Mathématique, _N_S_93 (2013) no. 107, p. 145 . http://geodesic.mathdoc.fr/item/PIM_2013_N_S_93_107_a11/