Remarks on extremally disconnected semitopological groups. (English) Zbl 1090.54033

Protasov, I. V.

Commentat. Math. Univ. Carol. 43, No. 2, 343-347 (2002).

Using results of I. V. Protasov [Sib. Math. J. 39, 1184–1194 (1998; Zbl 0935.22002)], an example of an extremally disconnected semitopological (i.e.left and right topological) group with continuous inverse is given in ZFC. This gives a negative answer to a question posed by A. V. Arhangel’skii. Several weaker examples (of non-discrete semitopological groups with continuous inverse) are derived easier from results of I. V. Protasov [Mat. Stud. 15, 9–22 (2001; Zbl 0989.22003)].

Reviewer: Petr Holický (Praha)

MSC:

54H11	Topological groups (topological aspects)
54C05	Continuous maps
54G15	Pathological topological spaces

Keywords:

extremally disconnected spaces; semitopological groups

Citations:

Zbl 0935.22002; Zbl 0989.22003