A topological group observation on the Banach–Mazur separable quotient problem

Topology and its Applications

Volumn 259, Issue , 2019, Pages 283-286

  Gabriyelyan, Saak S ^a   Morris, Sidney A ^b,c  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b UNIVERSITY OF BALLARAT   (Australia)

^c LA TROBE UNIVERSITY   (Australia)

Author keywords

Banach space; Circle group; Fr chet space; Locally convex space; Quotient group; Quotient space; Separable; Separable Quotient Problem; Topological group

Indexed keywords

EID: 85060598070     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2019.02.036     Document Type: Article

References (17)

1. Amir, D., Lindenstrauss, J., The structure of weakly compact sets in Banach spaces. Ann. Math. 88 (1968), 33–46.
2. Argyros, S.A., Dodos, P., Kanellopoulos, V., Unconditional families in Banach spaces. Math. Ann. 341 (2008), 15–38.
3. Becker, H., Kechris, A.S., The Descriptive Set Theory of Polish Group Actions. 1996, Cambridge University Press, Cambridge.
4. Bessaga, C., Pełczyński, A.A., Selected Topics in Infinite-Dimensional Topology. 1975, Polish Scientific Publishers, Warszawa, Poland.
5. Eidelheit, M., Zur Theorie der Systeme linearer Gleichungen. Stud. Math. 6 (1936), 130–148.
6. Gabriyelyan, S., Ka̧kol, J., Plebanek, G., The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces. Stud. Math. 233 (2016), 119–139.
7. Hewitt, E., Ross, K.A., Abstract Harmonic Analysis, vol. I. 2nd edition, 1979, Springer-Verlag, Berlin.
8. Hofmann, K.H., Morris, S.A., The Structure of Compact Groups. 3rd edition, 2013, De Gruyter, Berlin.
9. p(X), and their duals. Proc. Am. Math. Soc. 145 (2017), 3829–3841.
10. Ka̧kol, J., Saxon, S.A., Todd, A., Barrelled spaces with(out) separable quotients. Bull. Aust. Math. Soc. 90 (2014), 295–303.
11. Ka̧kol, J., Śliwa, W., Remarks concerning the separable quotient problem. Note Mat. 13 (1993), 277–282.
12. Leiderman, A.G., Morris, S.A., Tkachenko, M.G., The separable quotient problem for topological groups. Isr. J. Math., 2019 in press.
13. Pełczyński, A., Some problems on bases in Banach and Fréchet spaces. Isr. J. Math. 2 (1964), 132–138.
14. van Mill, J., The Infinite-Dimensional Topology of Function Spaces. 2006, Elsevier, North-Holland, Amsterdam.
15. Saxon, S.A., Narayanaswami, P.P., Metrizable (LF)-spaces, (db)-spaces, and the separable quotient problem. Bull. Aust. Math. Soc. 23 (1981), 65–80.
16. Saxon, S., Wilansky, A., The equivalence of some Banach space problems. Colloq. Math. 37 (1977), 217–226.
17. Śliwa, W., Every infinite-dimensional non-archimedian Fréchet space has an orthogonal basic sequence. Indag. Math. 11 (2000), 463–466.