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Keywords:
sequence-covering; compact-covering; pseudo-sequence-covering; sequentially-quotient; $\pi $-mapping; $ls$-Ponomarev-system; double point-star cover
sequence-covering; compact-covering; pseudo-sequence-covering; sequentially-quotient; $\pi $-mapping; $ls$-Ponomarev-system; double point-star cover
Summary:
We use the $ls$-Ponomarev-system $(f, M, X, \lbrace \mathcal{P}_{\lambda ,n}\rbrace )$, where $M$ is a locally separable metric space, to give a consistent method to construct a $\pi $-mapping (compact mapping) with covering-properties from a locally separable metric space $M$ onto a space $X$. As applications of these results, we systematically get characterizations of certain $\pi $-images (compact images) of locally separable metric spaces.
References:
[1] An, T. V., Dung, N. V.: On $\pi $–images of locally separable metric spaces. Internat. J. Math. Math. Sci. (2008), 1–8. DOI 10.1155/2008/145683 | Zbl 1147.54318
[2] An, T. V., Dung, N. V.: On $ls$–Ponomarev systems and $s$–images of locally separable metric spaces. Lobachevskii J. Math. 29 (2008 (3)), 111–118. DOI 10.1134/S1995080208030013 | MR 2434889 | Zbl 1168.54013
[3] Arhangel’skii, A. V.: Mappings and spaces. Russian Math. Surveys 21 (1966), 115–162. DOI 10.1070/RM1966v021n04ABEH004169 | MR 0227950
[4] Boone, J. R., Siwiec, F.: Sequentially quotient mappings. Czechoslovak Math. J. 26 (1976), 174–182. MR 0402689 | Zbl 0334.54003
[5] Engelking, R.: General topology. PWN – Polish Scientific Publishers, Warsaw, 1977. MR 0500780 | Zbl 0373.54002
[6] Ge, Y.: On compact images of locally separable metric spaces. Topology Proc. 27 (1) (2003), 351–360. MR 2048944 | Zbl 1072.54020
[7] Ge, Y.: On pseudo–sequence–covering $\pi $–images of metric spaces. Mat. Vesnik 57 (2005), 113–120. MR 2194600
[8] Ge, Y.: On three equivalences concerning Ponomarev–systems. Arch. Math. (Brno) 42 (2006), 239–246. MR 2260382 | Zbl 1164.54363
[9] Ikeda, Y., Liu, C., Tanaka, Y.: Quotient compact images of metric spaces, and related matters. Topology Appl. 122 (2002), 237–252. DOI 10.1016/S0166-8641(01)00145-6 | MR 1919303 | Zbl 0994.54015
[10] Li, Z.: On $\pi $–$s$–images of metric spaces. nternat. J. Math. Math. Sci. 7 (2005), 1101–1107. DOI 10.1155/IJMMS.2005.1101 | Zbl 1082.54023
[11] Lin, S.: Point-countable covers and sequence-covering mappings. Chinese Science Press, Beijing, 2002. MR 1939779 | Zbl 1004.54001
[12] Lin, S., Liu, C, Dai, M.: Images on locally separable metric spaces. Acta Math. Sinica (N.S.) 13 (1) (1997), 1–8. DOI 10.1007/BF02560519 | MR 1465530 | Zbl 0881.54014
[13] Lin, S., Yan, P.: Notes on $cfp$-covers. Comment. Math. Univ. Carolin. 44 (2) (2003), 295–306. MR 2026164 | Zbl 1100.54021
[14] Michael, E.: A note on closed maps and compact subsets. Israel J. Math. 2 (1964), 173–176. DOI 10.1007/BF02759940 | MR 0177396
[15] Michael, E.: $\aleph _0$–spaces. J. Math. Mech. 15 (1966), 983–1002. MR 0206907
[16] Ponomarev, V. I.: Axiom of countability and continuous mappings. Bull. Polish Acad. Sci. Math. 8 (1960), 127–133. MR 0116314
[17] Siwiec, F.: Sequence-covering and countably bi–quotient mappings. General Topology Appl. 1 (1971), 143–154. DOI 10.1016/0016-660X(71)90120-6 | MR 0288737 | Zbl 0218.54016
[18] Tanaka, Y.: Theory of $k$–networks II. Questions Answers Gen. Topology 19 (2001), 27–46. MR 1815344 | Zbl 0970.54023
[19] 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
[20] Yan, P.: On the compact images of metric spaces. J. Math. Study 30 (2) (1997), 185–187. MR 1468151
[21] Yan, P.: On strong sequence–covering compact mappings. Northeast. Math. J. 14 (1998), 341–344. MR 1685267 | Zbl 0927.54030
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