Geodesic
On $k$-spaces and $k_R$-spaces
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 941-945
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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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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/

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