| Title:
|
On a problem of Nogura about the product of Fréchet-Urysohn $\langle \alpha_4\rangle$-spaces (English) |
| Author:
|
Costantini, Camillo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
537-549 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Assuming Martin's Axiom, we provide an example of two Fréchet-Urysohn $\langle\alpha_4\rangle$-spaces, whose product is a non-Fréchet-Urysohn $\langle\alpha_4\rangle$-space. This gives a consistent negative answer to a question raised by T. Nogura. (English) |
| Keyword:
|
Fréchet-Urysohn space |
| Keyword:
|
$\langle\alpha_4\rangle$-space |
| Keyword:
|
Martin's Axiom |
| Keyword:
|
almost disjoint functions |
| Keyword:
|
double iterated power |
| MSC:
|
03E50 |
| MSC:
|
54A20 |
| MSC:
|
54A35 |
| MSC:
|
54B10 |
| MSC:
|
54D55 |
| MSC:
|
54D80 |
| MSC:
|
54G15 |
| MSC:
|
54G20 |
| idZBL:
|
Zbl 1010.54041 |
| idMR:
|
MR1732482 |
| . |
| Date available:
|
2009-01-08T18:55:04Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119109 |
| . |
| Reference:
|
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| Reference:
|
[Ar2] Arhangel'skii A.V.: The frequency spectrum of a topological space and the product operation.Transl. Moscow Math. Soc., Issue 2 (1981), 163-200. |
| Reference:
|
[CS] Costantini C., Simon P.: An $\alpha_4$, not Fréchet product of $\alpha_4$ Fréchet spaces.Topology Appl., to appear. Zbl 0959.54006, MR 1783423 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
[Si2] Simon P.: A hedgehog in a product.Acta Univ. Carolin.-Math. Phys., to appear. Zbl 1007.54023, MR 1696588 |
| . |
