| Title:
|
Further properties of 1-sequence-covering maps (English) |
| Author:
|
An, Tran Van |
| Author:
|
Tuyen, Luong Quoc |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
477-484 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some relationships between $1$-sequence-covering maps and weak-open maps or sequence-covering $s$-maps are discussed. These results are used to generalize a result from Lin S., Yan P., {\it Sequence-covering maps of metric spaces\/}, Topology Appl. {\bf 109} (2001), 301--314. (English) |
| Keyword:
|
weak base |
| Keyword:
|
$sn$-network |
| Keyword:
|
sequence-covering |
| Keyword:
|
$1$-sequence-covering |
| Keyword:
|
weak-open |
| Keyword:
|
$\pi$-$s$-map |
| MSC:
|
54C10 |
| MSC:
|
54D65 |
| MSC:
|
54E40 |
| MSC:
|
54E99 |
| idZBL:
|
Zbl 1212.54092 |
| idMR:
|
MR2490441 |
| . |
| Date available:
|
2009-05-05T17:12:30Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119737 |
| . |
| Reference:
|
[1] Arhangel'skii A.V.: Mappings and spaces.Russian Math. Surveys 21 4 (1966), 115-162. MR 0227950 |
| Reference:
|
[2] Davis S.W.: More on Cauchy conditions.Topology Proc. 9 (1984), 31-36. Zbl 0561.54020, MR 0781549 |
| Reference:
|
[3] Engelking R.: General Topology.PWN-Polish Scientific Publishers, Warszawa, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[4] Franklin S.P.: Spaces in which sequences suffice.Fund. Math. 57 (1965), 107-115. Zbl 0132.17802, MR 0180954 |
| Reference:
|
[5] Ge X.: Spaces with a locally countable $sn$-network.Lobachevskii J. Math. 26 (2007), 33-49. Zbl 1140.54009, MR 2396700 |
| Reference:
|
[6] Ge Y.: Characterizations of $sn$-metrizable spaces.Publ. Inst. Math. (Beograd) (N.S.) 74 (88) (2003), 121-128. MR 2066998, 10.2298/PIM0374121G |
| Reference:
|
[7] Ge Y.: Spaces with countable $sn$-networks.Comment. Math. Univ. Carolin. 45 1 (2004), 169-176. Zbl 1098.54025, MR 2076868 |
| Reference:
|
[8] Gruenhage G., Michael E., Tanaka Y.: Spaces determined by point-countable covers.Pacific J. Math. 113 2 (1984), 303-332. Zbl 0561.54016, MR 0749538, 10.2140/pjm.1984.113.303 |
| Reference:
|
[9] Ikeda Y., Tanaka Y.: Spaces having star-countable $k$-networks.Topology Proc. 18 (1993), 107-132. Zbl 0829.54018, MR 1305126 |
| Reference:
|
[10] Ikeda Y., Liu C., Tanaka Y.: Quotient compact images of metric spaces, and related matters.Topology Appl. 122 1-2 (2002), 237-252. Zbl 0994.54015, MR 1919303, 10.1016/S0166-8641(01)00145-6 |
| Reference:
|
[11] Li Z.: On $\pi$-$s$-images of metric spaces.Int. J. Math. Math. Sci. 7 (2005), 1101-1107. Zbl 1082.54023, MR 2170507, 10.1155/IJMMS.2005.1101 |
| Reference:
|
[12] Li Z., Lin S.: On the weak-open images of metric spaces.Czechoslovak Math. J. 54 (2004), 939-400. Zbl 1080.54509, MR 2059259 |
| Reference:
|
[13] Lin S.: Generalized Metric Spaces and Mappings.Chinese Science Press, Beijing, 1995 (Chinese). MR 1375020 |
| Reference:
|
[14] Lin S.: On sequence-covering $s$-mappings.Adv. Math. (China) 25 6 (1996), 548-551. Zbl 0864.54026, MR 1453163 |
| Reference:
|
[15] Lin S.: Point-Countable Covers and Sequence-Covering Mappings.Chinese Science Press, Beijing, 2002. Zbl 1004.54001, MR 1939779 |
| Reference:
|
[16] Lin S., Yan P.: Sequence-covering maps of metric spaces.Topology Appl. 109 (2001), 301-314. Zbl 0966.54012, MR 1807392, 10.1016/S0166-8641(99)00163-7 |
| Reference:
|
[17] Liu C.: On weak bases.Topology Appl. 150 (2005), 91-99. Zbl 1081.54026, MR 2133670, 10.1016/j.topol.2004.11.008 |
| Reference:
|
[18] O'Meara P.: On paracompactness in function spaces with the compact-open topology.Proc. Amer. Math. Soc. 29 (1971), 183-189. Zbl 0214.21105, MR 0276919, 10.2307/2037695 |
| Reference:
|
[19] Michael E.: $\aleph_0$-spaces.J. Math. Mech. 15 (1966), 983-1002. MR 0206907 |
| Reference:
|
[20] Siwiec F.: On defining a space by a weak base.Pacific J. Math. 52 (1974), 233-245. Zbl 0285.54022, MR 0350706, 10.2140/pjm.1974.52.233 |
| Reference:
|
[21] Tanaka Y.: Point-countable covers and $k$-networks.Topology Proc. 12 (1987), 327-349. Zbl 0676.54035, MR 0991759 |
| Reference:
|
[22] Tanaka Y.: Theory of $k$-networks II.Questions Answers Gen. Topology 19 (2001), 27-46. Zbl 0970.54023, MR 1815344 |
| Reference:
|
[23] Tanaka Y., Ge Y.: Around quotient compact images of metric spaces, and symmetric spaces.Houston J. Math. 32 1 (2006), 99-117. Zbl 1102.54034, MR 2202355 |
| Reference:
|
[24] Yan P.: On strong sequence-covering compact mappings.Northeastern Math. J. 14 (1998), 341-344. Zbl 0927.54030, MR 1685267 |
| Reference:
|
[25] Xia S.: Characterizations of certain $g$-first countable spaces.Adv. Math. (China) 29 (2000), 61-64. Zbl 0999.54010, MR 1769127 |
| . |
