Products of topological groups in which all closed subgroups are separable

Topology and its Applications

Volumn 241, Issue , 2018, Pages 89-101

  Leiderman, Arkady G ^a   Tkachenko, Mikhail G ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b DEPARTAMENTO DE QUÍMICA   (Mexico)

Author keywords

Closed subgroup; Locally convex space; Pseudocompact; Pseudocomplete; Separable; Topological group

Indexed keywords

EID: 85044957534     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2018.03.022     Document Type: Article

References (19)

1. Arhangel'skii, Alexander V., Tkachenko, Mikhail G., Topological Groups and Related Structures. Atlantis Series in Mathematics, vol. I, 2008, Atlantis Press/World Scientific Publishing Co. Pte. Ltd., Paris/Hackensack, NJ.
2. Pérez Carreras, Pedro, Bonet, José Barreled locally convex spaces. Nachbin, L., (eds.) North-Holland Math. Studies, Notas de Matemática, vol. 113, 1987, Elsevier Science Publishing.
3. Comfort, Wistar W., Itzkowitz, Gerald L., Density characters in topological groups. Math. Ann. 226 (1977), 223–227.
4. Dikranjan, Dikran N., Uspenskij, Vladimir V., Categorically compact topological groups. J. Pure Appl. Algebra 126:1–3 (1998), 149–168.
5. Domański, Pawel, Nonseparable closed subspaces in separable products of topological vector spaces, and q-minimality. Arch. Math. 41 (1983), 270–275.
6. Engelking, Richard, General Topology. 1989, Heldermann Verlag, Berlin.
7. Itzkowitz, Gerald L., On the density character of compact topological groups. Fundam. Math. 75 (1972), 201–203.
8. Klyachko, Anton A., Ol'shanskii, Alexander Yu., Osin, Denis V., On topologizable and non-topologizable groups. Topol. Appl. 160 (2013), 2104–2120.
9. Ka̧kol, Jerzy, Leiderman, Arkady G., Morris, Sidney A., Nonseparable closed vector subspaces of separable topological vector spaces. Monatshefte Math. 182 (2017), 39–47, 10.1007/s00605-016-0876-2.
10. Elton Lacey, H., The Hamel dimension of any infinite dimensional separable Banach space is c. Am. Math. Mon., 80(3), 1973, 298.
11. Leiderman, Arkady G., Morris, Sidney A., Tkachenko, Mikhail G., Density character of subgroups of topological groups. Trans. Am. Math. Soc. 369:8 (2017), 5645–5664, 10.1090/tran/6832.
12. Lohman, Robert H., Stiles, Wilbur J., On separability in linear topological spaces. Proc. Am. Math. Soc. 42 (1974), 236–237.
13. Lukács, Gábor, Hereditarily non-topologizable groups. Topol. Proc. 33 (2009), 269–275.
14. van Mill, Jan, Tkachuk, Vladimir V., Every k-separable Čech-complete space is subcompact. RACSAM 109 (2015), 65–71.
15. Morris, Sidney A., Pontryagin Duality and the Structure of Locally Compact Abelian Groups. 1977, Cambridge University Press, Cambridge–London–New York–Melbourne.
16. Oxtoby, John C., Cartesian products of Baire spaces. Fundam. Math. 49 (1961), 157–166.
17. Roitman, Judith, Basic S and L. Kunen, K., Vaughan, J., (eds.) Handbook of Set Theoretic Topology, 1984, North Holland, Amsterdam, 295–326 Chapter 7.
18. Rudin, Walter, Functional Analysis. 1991, McGraw-Hill.
19. Tkachenko, Mikhail G., The notion of o-tightness and C-embedded subsets of products. Topol. Appl. 15:1 (1983), 93–98.