Mapping theorems on ℵ -spaces

Masami Sakai

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 1, page 163-167
  • ISSN: 0010-2628

Abstract

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In this paper we improve some mapping theorems on ℵ -spaces. For instance we show that an ℵ -space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an ℵ -space is preserved by a closed and open map.

How to cite

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Sakai, Masami. "Mapping theorems on $\aleph $-spaces." Commentationes Mathematicae Universitatis Carolinae 49.1 (2008): 163-167. <http://eudml.org/doc/250293>.

@article{Sakai2008,
abstract = {In this paper we improve some mapping theorems on $\aleph $-spaces. For instance we show that an $\aleph $-space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an $\aleph $-space is preserved by a closed and open map.},
author = {Sakai, Masami},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\aleph $-space; $k$-network; closed map; countably bi-quotient map; -space; -network; closed map; countably bi-quotient map},
language = {eng},
number = {1},
pages = {163-167},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Mapping theorems on $\aleph $-spaces},
url = {http://eudml.org/doc/250293},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Sakai, Masami
TI - Mapping theorems on $\aleph $-spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 1
SP - 163
EP - 167
AB - In this paper we improve some mapping theorems on $\aleph $-spaces. For instance we show that an $\aleph $-space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an $\aleph $-space is preserved by a closed and open map.
LA - eng
KW - $\aleph $-space; $k$-network; closed map; countably bi-quotient map; -space; -network; closed map; countably bi-quotient map
UR - http://eudml.org/doc/250293
ER -

References

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  1. Gao Z.M., ℵ -space is invariant under perfect mappings, Questions Answers Gen. Topology 5 (1987), 271-279. (1987) Zbl0636.54026MR0917885
  2. Gao Z.M., Hattori Y., A characterization of closed s -images of metric spaces, Tsukuba J. Math. 11 (1987), 367-370. (1987) Zbl0643.54034MR0926463
  3. Junnila H., Ziqiu Y., 10.1016/0166-8641(92)90096-I, Topology Appl. 44 (1992), 209-215. (1992) MR1173260DOI10.1016/0166-8641(92)90096-I
  4. Lin S., 10.1016/0166-8641(88)90014-4, Topology Appl. 30 (1988), 159-164. (1988) Zbl0663.54017MR0967752DOI10.1016/0166-8641(88)90014-4
  5. Liu C., Notes on closed mappings, Houston J. Math. 33 (2007), 249-259. (2007) Zbl1133.54018MR2287853
  6. Liu C., Sakai M., Tanaka Y., 10.1016/S0166-8641(01)00066-9, Topology Appl. 119 (2002), 209-217. (2002) Zbl0997.54059MR1886095DOI10.1016/S0166-8641(01)00066-9
  7. O'Meara P., 10.2307/2037695, Proc. Amer. Math. Soc. 29 (1971), 183-189. (1971) Zbl0214.21105MR0276919DOI10.2307/2037695
  8. Siwiec F., 10.1016/0016-660X(71)90120-6, General Topology Appl. 1 (1971), 143-154. (1971) Zbl0218.54016MR0288737DOI10.1016/0016-660X(71)90120-6
  9. Siwiec F., Mancuso V.J., 10.1016/0016-660X(71)90108-5, General Topology Appl. 1 (1971), 33-41. (1971) Zbl0216.44203MR0282347DOI10.1016/0016-660X(71)90108-5
  10. Tanaka Y., Point-countable covers and k -networks, Topology Proc. 12 (1987), 327-349. (1987) Zbl0676.54035MR0991759
  11. Ziqiu Y., A new characterization of ℵ -spaces, Topology Proc. 16 (1991), 253-256. (1991) Zbl0784.54029

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