Geodesic
On $k$-spaces and $k_R$-spaces
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 941-945 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this note we study the relation between $k_R$-spaces and $k$-spaces and prove that a $k_R$-space with a $\sigma $-hereditarily closure-preserving $k$-network consisting of compact subsets is a $k$-space, and that a $k_R$-space with a point-countable $k$-network consisting of compact subsets need not be a $k$-space.
In this note we study the relation between $k_R$-spaces and $k$-spaces and prove that a $k_R$-space with a $\sigma $-hereditarily closure-preserving $k$-network consisting of compact subsets is a $k$-space, and that a $k_R$-space with a point-countable $k$-network consisting of compact subsets need not be a $k$-space.
Classification : 54C30, 54D50
Keywords: $k_R$-spaces; $k$-spaces; $k$-networks; $\sigma $-hereditarily closure-preserving collections; point-countable collections 
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     author = {Li, Jinjin},
     title = {On $k$-spaces and $k_R$-spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {941--945},
     year = {2005},
     volume = {55},
     number = {4},
     mrnumber = {2184375},
     zbl = {1081.54021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a10/}
}
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Li, Jinjin. On $k$-spaces and $k_R$-spaces. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 941-945. http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a10/