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Fréchet property in compact spaces is not preserved by M -equivalence

Oleg Okunev

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 4, page 747-749
  • ISSN: 0010-2628

Abstract

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An example of two M -equivalent (hence l -equivalent) compact spaces is presented, one of which is Fréchet and the other is not.

How to cite

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Okunev, Oleg. "Fréchet property in compact spaces is not preserved by $M$-equivalence." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 747-749. <http://eudml.org/doc/249515>.

@article{Okunev2005,
abstract = {An example of two $M$-equivalent (hence $l$-equivalent) compact spaces is presented, one of which is Fréchet and the other is not.},
author = {Okunev, Oleg},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$l$-equivalence; $M$-equivalence; Fréchet property; -equivalence; -equivalence},
language = {eng},
number = {4},
pages = {747-749},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Fréchet property in compact spaces is not preserved by $M$-equivalence},
url = {http://eudml.org/doc/249515},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Okunev, Oleg
TI - Fréchet property in compact spaces is not preserved by $M$-equivalence
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 4
SP - 747
EP - 749
AB - An example of two $M$-equivalent (hence $l$-equivalent) compact spaces is presented, one of which is Fréchet and the other is not.
LA - eng
KW - $l$-equivalence; $M$-equivalence; Fréchet property; -equivalence; -equivalence
UR - http://eudml.org/doc/249515
ER -

References

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  1. Arhangel'skii A.V., On linear homeomorphisms of function spaces, Soviet Math. Doklady 25 (1982), 852-855. (1982) 
  2. 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. (1990) 
  3. Arhangel'skii A.V., Topological Function Spaces, Kluwer Acad. Publ. Dordrecht (1992). (1992) MR1485266
  4. Engelking R., General Topology, (1976), PWN Warszawa. (1976) Zbl0373.54001MR0500780
  5. 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). (1962) 
  6. Okunev O., A method for constructing examples of M-equivalent spaces, Topology Appl. 36 (1990), 157-171 Correction Topology Appl. 49 (1993), 191-192. (1993) Zbl0779.54008MR1068167
  7. Okunev O., Tightness of compact spaces is preserved by the t -equivalence relation, Comment. Mat. Univ. Carolinae 43 2 335-342 (2002). (2002) Zbl1090.54004MR1922131
  8. Simon P., A compact Fréchet space whose square is not Fréchet, Comment. Math. Univ. Carolinae 21 (1980), 749-753. (1980) Zbl0466.54022MR0597764
  9. 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. (1985) MR0790433

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