| Title:
|
Fréchet property in compact spaces is not preserved by $M$-equivalence (English) |
| Author:
|
Okunev, Oleg |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
747-749 |
| . |
| Category:
|
math |
| . |
| Summary:
|
An example of two $M$-equivalent (hence $l$-equivalent) compact spaces is presented, one of which is Fréchet and the other is not. (English) |
| Keyword:
|
$l$-equivalence |
| Keyword:
|
$M$-equivalence |
| Keyword:
|
Fréchet property |
| MSC:
|
54C35 |
| MSC:
|
54D30 |
| MSC:
|
54D99 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 1121.54033 |
| idMR:
|
MR2259504 |
| . |
| Date available:
|
2009-05-05T16:54:48Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119564 |
| . |
| Reference:
|
[Arh1] Arhangel'skii A.V.: On linear homeomorphisms of function spaces.Soviet Math. Doklady 25 (1982), 852-855. |
| Reference:
|
[Arh2] Arhangel'skii A.V.: Problems in $C_p$-theory.J. van Mill and G.M. Reed (1990), 601-615 Open Problems in Topology North-Holland Amsterdam. |
| Reference:
|
[Arh3] Arhangel'skii A.V.: Topological Function Spaces.Kluwer Acad. Publ. Dordrecht (1992). MR 1485266 |
| Reference:
|
[Eng] Engelking R.: General Topology.(1976), PWN Warszawa. Zbl 0373.54001, MR 0500780 |
| Reference:
|
[Mar] Markov A.A.: On free topological groups.Izv. Akad. Nauk SSSR Ser. Mat (1) (1945), Russian English transl.: Amer. Math. Soc. Transl. (1) 8 (1962). |
| Reference:
|
[Oku1] Okunev O.: A method for constructing examples of M-equivalent spaces.Topology Appl. 36 (1990), 157-171 Correction Topology Appl. 49 (1993), 191-192. Zbl 0779.54008, MR 1068167 |
| Reference:
|
[Oku2] Okunev O.: Tightness of compact spaces is preserved by the $t$-equivalence relation.Comment. Mat. Univ. Carolinae 43 2 335-342 (2002). Zbl 1090.54004, MR 1922131 |
| Reference:
|
[Sim] Simon P.: A compact Fréchet space whose square is not Fréchet.Comment. Math. Univ. Carolinae 21 (1980), 749-753. Zbl 0466.54022, MR 0597764 |
| Reference:
|
[Tka] Tkachuk V.V.: Duality with respect to the functor $C_p$ and cardinal invariants of the type of the Souslin number.Math. Notes (1985), 37 3-4 247-252. MR 0790433 |
| . |
