On k -spaces and k R -spaces

Jinjin Li

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 4, page 941-945
  • ISSN: 0011-4642

Abstract

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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 σ -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.

How to cite

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Li, Jinjin. "On $k$-spaces and $k_R$-spaces." Czechoslovak Mathematical Journal 55.4 (2005): 941-945. <http://eudml.org/doc/31001>.

@article{Li2005,
abstract = {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.},
author = {Li, Jinjin},
journal = {Czechoslovak Mathematical Journal},
keywords = {$k_R$-spaces; $k$-spaces; $k$-networks; $\sigma $-hereditarily closure-preserving collections; point-countable collections; -spaces; -spaces; -networks; -hereditarily closure-preserving collections; point-countable collections},
language = {eng},
number = {4},
pages = {941-945},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $k$-spaces and $k_R$-spaces},
url = {http://eudml.org/doc/31001},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Li, Jinjin
TI - On $k$-spaces and $k_R$-spaces
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 941
EP - 945
AB - 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.
LA - eng
KW - $k_R$-spaces; $k$-spaces; $k$-networks; $\sigma $-hereditarily closure-preserving collections; point-countable collections; -spaces; -spaces; -networks; -hereditarily closure-preserving collections; point-countable collections
UR - http://eudml.org/doc/31001
ER -

References

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  1. On complete topological linear spaces, Czechoslovak Math.  J. 3(78) (1953), 301–364. (Russian, English Summary) (1953) MR0064303
  2. On k -spaces, k R -spaces and k ( X ) , Pac. J.  Math. 47 (1973), 487–498. (1973) Zbl0262.54017MR0331328
  3. Note on k R -space, Quest. Answers Gen. Topology 9 (1991), 227–236. (1991) MR1113875
  4. On R -quotient s s -mappings, Acta Math. Sin. 34 (1991), 7–11. (Chinese) (1991) Zbl0760.54009MR1107584
  5. On k R -spaces and k -spaces, Adv. Math., Beijing 29 (2000), 223–226. (2000) Zbl0996.54037MR1789423
  6. On paracompactness in function spaces with the compact-open topology, Proc. Am. Math. Soc. 29 (1971), 183–189. (1971) MR0276919
  7. 10.1023/A:1015645107703, Acta Math. Hungar 95 (2002), 281–286. (2002) MR1909598DOI10.1023/A:1015645107703
  8. A stratifiable k R -space which is not a k -space, Proc. Am. Math. Soc. 81 (1981), 308–310. (1981) Zbl0447.54033MR0593478

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