Article
Keywords:
$l$-equivalence; $M$-equivalence; Fréchet property
Summary:
An example of two $M$-equivalent (hence $l$-equivalent) compact spaces is presented, one of which is Fréchet and the other is not.
References:
[Arh1] Arhangel'skii A.V.: On linear homeomorphisms of function spaces. Soviet Math. Doklady 25 (1982), 852-855.
[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.
[Arh3] Arhangel'skii A.V.:
Topological Function Spaces. Kluwer Acad. Publ. Dordrecht (1992).
MR 1485266
[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).
[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.
MR 1068167 |
Zbl 0779.54008
[Oku2] Okunev O.:
Tightness of compact spaces is preserved by the $t$-equivalence relation. Comment. Mat. Univ. Carolinae 43 2 335-342 (2002).
MR 1922131 |
Zbl 1090.54004
[Sim] Simon P.:
A compact Fréchet space whose square is not Fréchet. Comment. Math. Univ. Carolinae 21 (1980), 749-753.
MR 0597764 |
Zbl 0466.54022
[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