On the Ck -stable closure of the class of (separable) metrizable spaces

Monatshefte fur Mathematik

Volumn 180, Issue 1, 2016, Pages 39-64

  Banakh, T ^a,b   Gabriyelyan, S ^c  

^a IVAN FRANKO NATIONAL UNIVERSITY OF LVIV   (Ukraine)

^b JAN KOCHANOWSKI UNIVERSITY   (Poland)

^c BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Ascoli space; Ck stable closure; Function space; Metric space; P space; 0 space

Indexed keywords

EID: 84949527167     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-015-0840-6     Document Type: Article

References (23)

1. Banakh, T.: On topological groups containing a Frechet-Urysohn fan. Mat. Stud. 9, 149–154 (1998)
2. Banakh, T.: Topologies on groups determined by sequences: answers to several questions of I. Protasov and E. Zelenyuk. Mat. Stud. 2(15), 145–150 (2001)
3. 0 -spaces. Topol. Appl. 195, 151–173 (2015)
4. Banakh T.: Generalizations of k -spaces and their applications in general topology, function spaces, and Banach space theory (2015, preprint)
5. p -stable closure of the class of separable metrizable spaces. arXiv:1412.2240
6. Borges, C.: On stratifiable spaces. Pac. J. Math. 17, 1–16 (1966)
7. Engelking, R.: General topology. Heldermann Verlag, Berlin (1989)
8. c(X). Georgian Math. J. 20, 247–254 (2013)
9. Foged, L.: Characterizations of ℵ -spaces. Pac. J. Math. 110, 59–63 (1984)
10. Gabriyelyan, S.: Topologies on groups determined by sets of convergent sequences. J. Pure Appl. Algebra 217, 786–802 (2013)
11. k(X, 2). arXiv:1504.04198
12. Gabriyelyan, S., Kąkol, J.: On P -spaces and related concepts. Topol. Appl. 191, 178–198 (2015)
13. Gabriyelyan, S., Kąkol, J., Kubiś, W., Marciszewski, W.: Networks for the weak topology of Banach and Fréchet spaces. J. Math. Anal. Appl. 432, 1183–1199 (2015)
14. Gabriyelyan S., Kąkol J., Plebanek G.: The ascoli property for function spaces and the weak topology of Banach and Fréchet spaces. arXiv:1504.04202
15. Gruenhage G.: Generalized metric spaces. Handbook of set-theoretic topology, pp. 423–501. North-Holland, Amsterdam (1984)
16. Kechris, A.: Classical descriptive set theory. Springer-Verlag, New York (1995)
17. McCoy R.A., Ntantu I.: Topological properties of spaces of continuous functions. Lecture Notes in Math, vol. 1315 (1988)
18. O’Meara, P.: On paracompactness in function spaces with the compact-open topology. Proc. Am. Math. Soc. 29, 183–189 (1971)
19. 0 -spaces. J. Math. Mech. 15, 983–1002 (1966)
20. R -spaces and k(X). Pac. J. Math. 47, 487–498 (1973)
21. Noble, N.: Ascoli theorems and the exponential map. Trans. Am. Math. Soc. 143, 393–411 (1969)
22. Pol R.: A remark on a question of T. Banakh and S. Gabriyelyan, handwritten notes (2015)
23. k(X) for a class of separable metrizable X. Topol. Appl. 155, 2060–2062 (2008)