Glasnik Matematicki, Vol. 42, No.1 (2007), 89-94.

ON THE FUNDAMENTAL GROUP OF R3 MODULO THE CASE-CHAMBERLIN CONTINUUM

Katsuya Eda, Umed H. Karimov and Dušan Repovš

School of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
e-mail: eda@logic.info.waseda.ac.jp

Institute of Mathematics, Academy of Sciences of Tajikistan, Ul. Ainy 299A, Dushanbe 734063, Tajikistan
e-mail: umed-karimov@mail.ru

Institute of Mathematics, Physics and Mechanics and Faculty of Education, University of Ljubljana, P.O.Box 2964, Ljubljana 1001, Slovenia
e-mail: dusan.repovs@guest.arnes.si


Abstract.   It has been known for a long time that the fundamental group of the quotient of R3 by the Case-Chamberlin continuum is nontrivial. In the present paper we prove that this group is in fact, uncountable.

2000 Mathematics Subject Classification.   54F15, 55Q52, 57M05, 54B15, 54F35, 54G15.

Key words and phrases.   Case-Chamberlin continuum, quotient space, fundamental group, lower central series, weight, commutator.


Full text (PDF) (free access)

DOI: 10.3336/gm.42.1.07


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