Previous |  Up |  Next

Article

Keywords:
weak base; $sn$-network; sequence-covering; $1$-sequence-covering; weak-open; $\pi$-$s$-map
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.
References:
[1] Arhangel'skii A.V.: Mappings and spaces. Russian Math. Surveys 21 4 (1966), 115-162. MR 0227950
[2] Davis S.W.: More on Cauchy conditions. Topology Proc. 9 (1984), 31-36. MR 0781549 | Zbl 0561.54020
[3] Engelking R.: General Topology. PWN-Polish Scientific Publishers, Warszawa, 1977. MR 0500780 | Zbl 0684.54001
[4] Franklin S.P.: Spaces in which sequences suffice. Fund. Math. 57 (1965), 107-115. MR 0180954 | Zbl 0132.17802
[5] Ge X.: Spaces with a locally countable $sn$-network. Lobachevskii J. Math. 26 (2007), 33-49. MR 2396700 | Zbl 1140.54009
[6] Ge Y.: Characterizations of $sn$-metrizable spaces. Publ. Inst. Math. (Beograd) (N.S.) 74 (88) (2003), 121-128. DOI 10.2298/PIM0374121G | MR 2066998
[7] Ge Y.: Spaces with countable $sn$-networks. Comment. Math. Univ. Carolin. 45 1 (2004), 169-176. MR 2076868 | Zbl 1098.54025
[8] Gruenhage G., Michael E., Tanaka Y.: Spaces determined by point-countable covers. Pacific J. Math. 113 2 (1984), 303-332. DOI 10.2140/pjm.1984.113.303 | MR 0749538 | Zbl 0561.54016
[9] Ikeda Y., Tanaka Y.: Spaces having star-countable $k$-networks. Topology Proc. 18 (1993), 107-132. MR 1305126 | Zbl 0829.54018
[10] Ikeda Y., Liu C., Tanaka Y.: Quotient compact images of metric spaces, and related matters. Topology Appl. 122 1-2 (2002), 237-252. DOI 10.1016/S0166-8641(01)00145-6 | MR 1919303 | Zbl 0994.54015
[11] Li Z.: On $\pi$-$s$-images of metric spaces. Int. J. Math. Math. Sci. 7 (2005), 1101-1107. DOI 10.1155/IJMMS.2005.1101 | MR 2170507 | Zbl 1082.54023
[12] Li Z., Lin S.: On the weak-open images of metric spaces. Czechoslovak Math. J. 54 (2004), 939-400. MR 2059259 | Zbl 1080.54509
[13] Lin S.: Generalized Metric Spaces and Mappings. Chinese Science Press, Beijing, 1995 (Chinese). MR 1375020
[14] Lin S.: On sequence-covering $s$-mappings. Adv. Math. (China) 25 6 (1996), 548-551. MR 1453163 | Zbl 0864.54026
[15] Lin S.: Point-Countable Covers and Sequence-Covering Mappings. Chinese Science Press, Beijing, 2002. MR 1939779 | Zbl 1004.54001
[16] Lin S., Yan P.: Sequence-covering maps of metric spaces. Topology Appl. 109 (2001), 301-314. DOI 10.1016/S0166-8641(99)00163-7 | MR 1807392 | Zbl 0966.54012
[17] Liu C.: On weak bases. Topology Appl. 150 (2005), 91-99. DOI 10.1016/j.topol.2004.11.008 | MR 2133670 | Zbl 1081.54026
[18] O'Meara P.: On paracompactness in function spaces with the compact-open topology. Proc. Amer. Math. Soc. 29 (1971), 183-189. DOI 10.2307/2037695 | MR 0276919 | Zbl 0214.21105
[19] Michael E.: $\aleph_0$-spaces. J. Math. Mech. 15 (1966), 983-1002. MR 0206907
[20] Siwiec F.: On defining a space by a weak base. Pacific J. Math. 52 (1974), 233-245. DOI 10.2140/pjm.1974.52.233 | MR 0350706 | Zbl 0285.54022
[21] Tanaka Y.: Point-countable covers and $k$-networks. Topology Proc. 12 (1987), 327-349. MR 0991759 | Zbl 0676.54035
[22] Tanaka Y.: Theory of $k$-networks II. Questions Answers Gen. Topology 19 (2001), 27-46. MR 1815344 | Zbl 0970.54023
[23] Tanaka Y., Ge Y.: Around quotient compact images of metric spaces, and symmetric spaces. Houston J. Math. 32 1 (2006), 99-117. MR 2202355 | Zbl 1102.54034
[24] Yan P.: On strong sequence-covering compact mappings. Northeastern Math. J. 14 (1998), 341-344. MR 1685267 | Zbl 0927.54030
[25] Xia S.: Characterizations of certain $g$-first countable spaces. Adv. Math. (China) 29 (2000), 61-64. MR 1769127 | Zbl 0999.54010
Partner of
EuDML logo