| Title:
|
On the preservation of separation axioms in products (English) |
| Author:
|
Grulović, Milan Z. |
| Author:
|
Kurilić, Miloš S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
713-721 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give sufficient and necessary conditions to be fulfilled by a filter $\Psi $ and an ideal $\Lambda $ in order that the $\Psi $-quotient space of the $\Lambda $-ideal product space preserves $T_k$-properties ($k=0,1,2,3,3\frac{1}{2}$) (``in the sense of the \L os theorem''). Tychonoff products, box products and ultraproducts appear as special cases of the general construction. (English) |
| Keyword:
|
separation axioms |
| Keyword:
|
box product |
| Keyword:
|
ultraproduct |
| Keyword:
|
ideal product topology |
| MSC:
|
54B10 |
| MSC:
|
54D10 |
| MSC:
|
54D15 |
| idZBL:
|
Zbl 0786.54009 |
| idMR:
|
MR1240193 |
| . |
| Date available:
|
2009-01-08T18:00:07Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118543 |
| . |
| Reference:
|
[1] Bankston P.: Ultraproducts in topology.Gen. Topology Appl. 7 (1977), 283-308. Zbl 0364.54005, MR 0458351 |
| Reference:
|
[2] van Douwen E.K.: The box product of countably many metrizable spaces need not be normal.Fundamenta Mathematicae LXXXVIII.2 (1975), 127-132. MR 0385781 |
| Reference:
|
[3] Engelking R.: General Topology.PWN - Polish Scientific Publishers, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[4] Kelly J.L.: General Topology.Springer Verlag, Graduate Texts in Mathematics 27. |
| Reference:
|
[5] Knight C.J.: Box topologies.Quart. J. Math. Oxford 15 (1964), 41-54. Zbl 0122.17404, MR 0160184 |
| . |
