Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
rectifiable space; strongly topological gyrogroup; topological gyrogroup; topological group; sequential space; Fréchet--Urysohn space
rectifiable space; strongly topological gyrogroup; topological gyrogroup; topological group; sequential space; Fréchet--Urysohn space
Summary:
We give conditions for a sequential rectifiable space to be Fréchet--Urysohn. Moreover, we give a property of a Fréchet-Urysohn rectifiable space. By these results, we obtain some results related to (strongly) topological gyrogroups and topological groups.
References:
[1] Atiponrat W.: Topological gyrogroups: generalization of topological groups. Topology Appl. 224 (2017), 73–82. DOI 10.1016/j.topol.2017.04.004
[2] Bao M.: On strongly topological gyrogroup. Filomat 38 (2024), no. 8, 2821–2833.
[3] Bao M., Lin F.: Feathered gyrogroups and gyrogroups with countable pseudocharacter. Filomat 33 (2019), no. 16, 5113–5124. DOI 10.2298/FIL1916113B
[4] Bao M., Xu X.: A note on (strongly) topological gyrogroups. Topology Appl. 307 (2022), Paper No. 107950, 18 pages.
[5] Birkhoff G.: A note on topological groups. Compositio Math. 3 (1936), 427–430.
[6] Cai Z., Lin S., He W.: A note on paratopological loops. Bull. Malays. Math. Sci. Soc. 42 (2019), no. 5, 2535–2547. DOI 10.1007/s40840-018-0616-y
[7] Choban M. M.: On topological homogeneous algebras. in: Interim Reports of II Prague Topol. Symp. Prague, (1987), 25–26.
[8] Čhoban M. M.: The structure of locally compact algebras. Serdica 18 (1992), no. 3–4, 129–137.
[9] Engelking R.: General Topology. Sigma Series in Pure Mathematics, 6, Heldermann Verlag, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[10] Gul'ko A. S.: Rectifiable spaces. Topology Appl. 68 (1996), no. 2, 107–112. DOI 10.1016/0166-8641(95)00027-5
[11] Lin F., Liu C., Lin S.: A note on rectifiable spaces. Topology Appl. 159 (2012), no. 8, 2090–2101.
[12] Nyikos P. J.: Metrizability and the Fréchet–Urysohn property in topological groups. Proc. Amer. Math. Soc. 83 (1981), no. 4, 793–801.
[13] Tuyen L. Q., Tuyen O. V.: Some properties of rectifiable spaces. Fasciculi Math. 60 (2018), 181–190. DOI 10.1515/fascmath-2018-0012
[14] Uspenskiĭ V. V.: Topological groups and Dugundji compact spaces. Mat. Sb. 180 (1989), no. 8, 1092–1118 (Russian); translated in: Math. USSR-Sb. 67 (1990), no. 2, 555–580.
Search
Partner of
