| Title:
|
Two-fold theorem on Fréchetness of products (English) |
| Author:
|
Dolecki, S. |
| Author:
|
Nogura, T. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
421-429 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A refined common generalization of known theorems (Arhangel’skii, Michael, Popov and Rančin) on the Fréchetness of products is proved. A new characterization, in terms of products, of strongly Fréchet topologies is provided. (English) |
| Keyword:
|
$\alpha_3$ |
| Keyword:
|
$\alpha_4$ |
| Keyword:
|
$\beta_3$ |
| Keyword:
|
$\beta_4$ spaces |
| Keyword:
|
$\Phi$-space |
| Keyword:
|
product space |
| Keyword:
|
sequential space |
| Keyword:
|
sequentially subtransverse |
| Keyword:
|
strongly Fréchet |
| Keyword:
|
transverse |
| MSC:
|
54A20 |
| MSC:
|
54B10 |
| MSC:
|
54D50 |
| MSC:
|
54D55 |
| MSC:
|
54G15 |
| idZBL:
|
Zbl 0949.54010 |
| idMR:
|
MR1692508 |
| . |
| Date available:
|
2009-09-24T10:23:59Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127498 |
| . |
| Reference:
|
[1] A. V. Arhangel’skii: The frequency spectrum of a topological space and the product operation.Trans. Moscow Math. Soc. (1981), 164–200. |
| Reference:
|
[2] S. Dolecki and S. Sitou: Precise bounds for sequential order of products of some Fréchet topologies.Topology Appl. (to appear). MR 1611269 |
| Reference:
|
[3] E. K. van Douwen: The product of a Fréchet space and a metrizable space.Topology Appl. 47 (1992), 163–164. Zbl 0759.54013, MR 1192305, 10.1016/0166-8641(92)90026-V |
| Reference:
|
[4] R. Engelking: General Topology.PWN Warszawa (1977). Zbl 0373.54002, MR 0500780 |
| Reference:
|
[5] E. Michael: A quintuple quotient quest.General Topology Appl. 2 (1972), 91–138. Zbl 0238.54009, MR 0309045, 10.1016/0016-660X(72)90040-2 |
| Reference:
|
[6] E. Michael: A note on closed maps and compact sets.Israel J. Math. 2 (1964), 174–176. Zbl 0136.19303, MR 0177396 |
| Reference:
|
[7] T. Nogura: Fréchetness of inverse limits and products.Topology and Appl. 20 (1985), 59–66. Zbl 0605.54019, MR 0798445, 10.1016/0166-8641(85)90035-5 |
| Reference:
|
[8] T. Nogura: The product of $\langle \alpha _i\rangle $-spaces.Topology and Appl. 21 (1985), 251–259. MR 0812643 |
| Reference:
|
[9] J. Novák: On convergence group.Czechoslovak Math. J. 20 (1970), 357–374. MR 0263973 |
| Reference:
|
[10] P. Nyikos: The Cantor tree and the Fréchet-Urysohn property.Annals N.Y. Acad. Sc. 552 (1989), 109–123. Zbl 0894.54021, MR 1020779, 10.1111/j.1749-6632.1989.tb22391.x |
| Reference:
|
[11] P. Nyikos: Subsets of $^\omega \omega $ and the Fréchet-Urysohn and $\alpha _i$-properties.Topology Appl. 48 (1992), 91–116. Zbl 0774.54019, MR 1195504, 10.1016/0166-8641(92)90021-Q |
| Reference:
|
[12] V. V Popov and D. V. Rančin: On certain strengthening of the property of Fréchet-Urysohn.Vest. Moscow Univ. 2 (1978), 75–80. |
| Reference:
|
[13] Y. Tanaka: Products of sequential spaces.Proc. Amer. Math. Soc. 54 (1976), 371–375. Zbl 0292.54025, MR 0397665, 10.1090/S0002-9939-1976-0397665-6 |
| . |
