| Title:
|
The ambient homeomorphy of certain function and sequence spaces (English) |
| Author:
|
Dijkstra, Jan J. |
| Author:
|
Mogilski, Jerzy |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
595-611 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider a number of sequence and function spaces that are known to be homeomorphic to the countable product of the linear space $\sigma$. The spaces we are interested in have a canonical imbedding in both a topological Hilbert space and a Hilbert cube. It turns out that when we consider these spaces as subsets of a Hilbert cube then there is only one topological type. For imbeddings in the countable product of lines there are two types depending on whether the space is contained in a $\sigma$-compactum or not. (English) |
| Keyword:
|
Hilbert space |
| Keyword:
|
Hilbert cube |
| Keyword:
|
$\Cal F_{\sigma\delta}$-absorber |
| Keyword:
|
ambient homeomorphism |
| Keyword:
|
function space |
| Keyword:
|
$p$-summable sequence |
| MSC:
|
54C35 |
| MSC:
|
57N17 |
| MSC:
|
57N20 |
| idZBL:
|
Zbl 0881.57018 |
| idMR:
|
MR1426924 |
| . |
| Date available:
|
2009-01-08T18:26:27Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118866 |
| . |
| Reference:
|
[1] Baars J., Gladdines H., van Mill J.: Absorbing systems in infinite-dimensional manifolds.Topology Appl. 50 (1993), 147-182. Zbl 0794.57005, MR 1217483 |
| Reference:
|
[2] Bessaga C., Pełczyński A.: Selected Topics in Infinite-Dimensional Topology.PWN Warsaw (1975). |
| Reference:
|
[3] Curtis D.W.: Boundary sets in the Hilbert cube.Topology Appl. 20 (1985), 201-221. Zbl 0575.57008, MR 0804034 |
| Reference:
|
[4] Dijkstra J.J., Dobrowolski T., Marciszewski W., van Mill J., Mogilski J.: Recent classification and characterization results in geometric topology.Bull. Amer. Math. Soc. 22 (1990), 277-283. Zbl 0713.57011, MR 1027899 |
| Reference:
|
[5] Dijkstra J.J., van Mill J., Mogilski J.: The space of infinite-dimensional compacta and other topological copies of $(l^2_{an f})^ømega$.Pacific. J. Math. 152 (1992), 255-273. MR 1141795 |
| Reference:
|
[6] Dijkstra J.J., Mogilski J.: The topological product structure of systems of Lebesgue spaces.Math. Ann. 290 (1991), 527-543. Zbl 0734.46013, MR 1116236 |
| Reference:
|
[7] Dobrowolski T., Marciszewski W., Mogilski J.: On topological classification of function spaces $C_{an p}(X)$ of low Borel complexity.Trans. Amer. Math. Soc. 328 (1991), 307-324. MR 1065602 |
| Reference:
|
[8] Dobrowolski T., Mogilski J.: Problems on topological classification of incomplete metric spaces.409-429 in Open Problems in Topology, J. van Mill and G.M. Reed, eds., North-Holland, Amsterdam, 1990. MR 1078661 |
| Reference:
|
[9] Dobrowolski T., Mogilski J.: Certain sequence and function spaces homeomorphic to the countable product of $l_f^2$.J. London Math. Soc. 45.2 (1992), 566-576. MR 1180263 |
| Reference:
|
[10] Lutzer D., McCoy R.: Category in function spaces I.Pacific J. Math. 90 (1980), 145-168. Zbl 0481.54017, MR 0599327 |
| Reference:
|
[11] van Mill J.: Topological equivalence of certain function spaces.Compositio Math. 63 (1987), 159-188. Zbl 0634.54011, MR 0906368 |
| Reference:
|
[12] van Mill J.: Infinite-Dimensional Topology, Prerequisites and Introduction.North-Holland Amsterdam (1989). Zbl 0663.57001, MR 0977744 |
| . |
