| Title:
|
Characterizations of absolute $F_{\sigma\delta}$-sets (English) |
| Author:
|
Junnila, H. J. K. |
| Author:
|
Künzi, H. P. A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
55-64 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Keyword:
|
metric space |
| Keyword:
|
$F_{\sigma \delta }$-set |
| Keyword:
|
bicomplete quasi-metric |
| Keyword:
|
complete sequence of covers |
| Keyword:
|
compact family of sets |
| Keyword:
|
cotopology |
| MSC:
|
54E15 |
| MSC:
|
54E35 |
| MSC:
|
54E50 |
| MSC:
|
54H05 |
| idZBL:
|
Zbl 0926.54018 |
| idMR:
|
MR1614072 |
| . |
| Date available:
|
2009-09-24T10:10:59Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127398 |
| . |
| Reference:
|
[AGD1] J. M. Aarts, J. de Groot and R. H. McDowell: Cocompactness.Nieuw Arch. Wisk. 18 (1970), 2–15. MR 0268851 |
| Reference:
|
[AGD] J. M. Aarts, J. de Groot and R. H. McDowell: Cotopology for metrizable spaces.Duke Math. J. 37 (1970), 291–295. MR 0259859, 10.1215/S0012-7094-70-03737-3 |
| Reference:
|
[A] A. V. Arhangel’skij: On topological spaces which are complete in the sense of Čech.Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2 (1961), 37–40 (in Russian). MR 0131258 |
| Reference:
|
[Bi] R. H. Bing: Extending a metric.Duke Math. J. 14 (1947), 511–519. Zbl 0030.08003, MR 0024609, 10.1215/S0012-7094-47-01442-7 |
| Reference:
|
[C] E. Čech: On bicompact spaces.Annals of Math. 38 (1937), 823–844. MR 1503374, 10.2307/1968839 |
| Reference:
|
[D] J. Deák: Extending a quasi-metric.Studia Sci. Math. Hung. 28 (1993), 105–113. MR 1250800 |
| Reference:
|
[DGLM] J. Dijkstra, T. Grilliot, D. Lutzer and J. van Mill: Function spaces of low Borel complexity.Proc. Amer. Math. Soc. 94 (1985), 703–710. MR 0792287, 10.1090/S0002-9939-1985-0792287-2 |
| Reference:
|
[vE] F. van Engelen: Countable products of zero-dimensional absolute $F_{\sigma \delta }$ spaces.Indag. Math. 46 (1984), 391–399. MR 0770725 |
| Reference:
|
[E] R. Engelking: General Topology.Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[FK] N. Ferrario and H. P.A. Künzi: Bicompleteness of the fine quasi-uniformity.Math. Proc. Camb. Phil. Soc. 109 (1991), 167–186. MR 1075129, 10.1017/S0305004100069644 |
| Reference:
|
[FL] P. Fletcher and W. F. Lindgren: Quasi-uniform Spaces.Marcel Dekker, New York, 1982. MR 0660063 |
| Reference:
|
[F1] Z. Frolík: Generalizations of the $G_\delta $-property of complete metric spaces.Czech. Math. J. 10 (1960), 359–379. MR 0116305 |
| Reference:
|
[F2] Z. Frolík: On the descriptive theory of sets.Czech. Math. J. 13 (1963), 335–359. MR 0162215 |
| Reference:
|
[H] R. W. Hansell: General embedding properties of absolute Borel and Souslin spaces.Proc. Amer. Math. Soc. 27 (1971), 343–352. Zbl 0212.55202, MR 0268853, 10.1090/S0002-9939-1971-0268853-X |
| Reference:
|
[J1] H. J. K. Junnila: Neighbornets.Pacific J. Math. 76 (1978), 83–108. Zbl 0353.54016, MR 0482677 |
| Reference:
|
[J2] H. J. K. Junnila: On $\sigma $-spaces and pseudometrizable spaces.Topology Proceedings 4 (1979), 121–132. MR 0583695 |
| Reference:
|
[J3] H. J. K. Junnila: On strongly zero-dimensional $F_\sigma $-metrizable stratifiable spaces.In: Topology. General and Algebraic Topology, and Applications (Proc. Internat. Topological. Confer. Leningrad, 1982), L. D. Faddeev and A. A. Mal’cev (eds.), Lecture Notes in Math. 1060, Springer Verlag, Berlin, 1984, pp. 67–75. MR 0770226 |
| Reference:
|
[K] H. P. A. Künzi: On strongly quasi-metrizable spaces.Arch. Math. (Basel) 41 (1983), 57–63. 10.1007/BF01193823 |
| Reference:
|
[KRS] H. P. A. Künzi, S. Romaguera and S. Salbany: Topological spaces that admit bicomplete quasi-pseudometrics.Ann. Sci. Budapest 37 (1994), 185–195. MR 1303429 |
| Reference:
|
[RS] S. Romaguera and S. Salbany: On bicomplete quasi-pseudometrizability.Top. Appl. 50 (1993), 283–289. MR 1227555 |
| Reference:
|
[Si] W. Sierpiński: Sur une définition topologique des ensembles $F_{\sigma \delta }$.Fund. Math. 6 (1924), 24–29. 10.4064/fm-6-1-24-29 |
| Reference:
|
[St] A. H. Stone: Borel and analytic metric spaces.Proc. Washington State Univ. Confer. on Gen. Topology, Pi Mu Epsilon. Washington Alpha Center, 1970, pp. 20–33. Zbl 0199.25804, MR 0268848 |
| . |
