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Keywords:
paratopological groups; topological groups; sequential neighborhood; networks; metrizable; compactifications; remainders
paratopological groups; topological groups; sequential neighborhood; networks; metrizable; compactifications; remainders
Summary:
In this paper, we discuss certain
networks on paratopological (or
topological) groups and give positive
or negative answers to the questions
in [Lin2013]. We also prove that a
non-locally compact, $k$-gentle
paratopological group is metrizable if
its remainder (in the Hausdorff
compactification) is
a Fréchet-Urysohn space with a
point-countable cs*-network, which
improves some theorems in
[Liu C., Metrizability of paratopological
$($semitopological$)$ groups,
Topology Appl. 159 (2012), 1415--1420],
[Liu C., Lin S., Generalized metric
spaces with algebraic structures,
Topology Appl. 157 (2010), 1966--1974].
References:
[1] Arhangel'skiĭ A.V.: Mappings and spaces. Russian Math. Surveys 21 (1966), 115–162. DOI 10.1070/RM1966v021n04ABEH004169 | MR 0227950
[2] Arhangel'skii A.V.: More on remainders close to metrizable spaces. Topology Appl. 154 (2007), 1084–1088. DOI 10.1016/j.topol.2006.10.008 | MR 2298623 | Zbl 1144.54001
[3] Arhangel'skii A.V.: Components of first-countablity and various kinds of pseudoopen mappings. Topology Appl. 158 (2011), 215–222. DOI 10.1016/j.topol.2010.10.013 | MR 2739892
[4] Arhangel'skii A.V., Choban M.M.: On remainders of rectifiable spaces. Topology Appl. 157 (2010), 789–799. DOI 10.1016/j.topol.2009.08.028 | MR 2585412
[5] Arhangel'skiĭ A.V., Okunev O.G., Pestov V.G.: Free topological groups over metrizable spaces. Topology Appl. 33 (1989), 63–76. DOI 10.1016/0166-8641(89)90088-6 | MR 1020983
[6] Arhangel'skii A.V., Tkachenko M.: Topological Groups and Related Structures. Atlantis Press and World Sci., Hackensack, NJ, 2008. MR 2433295
[7] Engelking R.: General Topology. PWN, Polish Scientific Pub., Warszawa, 1977. MR 0500780 | Zbl 0684.54001
[8] Franklin S.: Spaces in which sequences suffice. Fund. Math. 57 (1965), 107–115. MR 0180954 | Zbl 0168.43502
[9] Gruenhage G.: k-spaces and products of closed images of metric spaces. Proc. Amer. Math. Soc. 80 (1980), 478–482. MR 0581009 | Zbl 0453.54012
[10] Gruenhage G.: Generalized metric spaces. K. Kunen, J.E. Vaughan, eds., Handbook of Set-Theoretic Topology, North-Holland, 1984, pp. 423–501. MR 0776629 | Zbl 0794.54034
[11] Gruenhage G., Michael E., Tanaka Y.: Spaces determined by point-countable covers. Pacific J. Math. 113 (1984), no. 2, 303–332. DOI 10.2140/pjm.1984.113.303 | MR 0749538 | Zbl 0561.54016
[12] Lin S.: On sequence-covering s-maps. Math. Adv. (China) 25 (1996), 548–551. MR 1453163
[13] Lin F.: A note on paratopological groups with countable networks of sequential neighborhoods. Topology Proc. 41 (2013), 9–16. MR 2903277
[14] Liu C.: A note on paratopological groups. Comment. Math. Univ. Carolin. 47 (2006), no. 4, 633–640. MR 2337418 | Zbl 1150.54036
[15] Liu C.: Metrizability of paratopological (semitopological) groups. Topology Appl. 159 (2012), 1415–1420. DOI 10.1016/j.topol.2012.01.002 | MR 2879371 | Zbl 1235.54015
[16] Liu C., Lin S.: Generalized metric spaces with algebraic structures. Topology Appl. 157 (2010), 1966–1974. DOI 10.1016/j.topol.2010.04.010 | MR 2646429 | Zbl 1194.54038
[17] Michael E.: A quintuple quotient quest. General Topology Appl. 2 (1972), 91–138. DOI 10.1016/0016-660X(72)90040-2 | MR 0309045 | Zbl 0238.54009
[18] Ordman E., Smith-Thomas B.: Sequential conditions and free topological groups. Proc. Amer. Math. Soc. 79 (1980), no. 2, 319–326. DOI 10.1090/S0002-9939-1980-0565363-2 | MR 0565363 | Zbl 0446.22001
[19] Simon P.: Divergent sequences in compact Hausdorff spaces. Topology, Vol. II (Proc. Fourth Colloq., Budapest, 1978), pp. 1087–1094, Colloq. Math. Soc. János Bolyai, 23, North-Holland, Amsterdam-New York, 1980. MR 0588856 | Zbl 0439.54022
[20] Shiraki T.: M-spaces, their generalization and metrization theorems. Sci. Rep. Tokyo Kyoiku Daigaku A, 11 (1971), 57–67. MR 0305365 | Zbl 0233.54016
[21] Tanaka Y.: Point-countable covers and k-networks. Topology Proc. 12 (1987), 327–349. MR 0991759 | Zbl 0676.54035
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