Two non-homeomorphic countable spaces having homeomorphic squares. (English) Zbl 0591.54006

Marjanović, M. M.; Vučemilović, A. R.

Commentat. Math. Univ. Carol. 26, 579-588 (1985).

The authors construct two countable, metrizable spaces X and Y such that \(X\times X\) is homeomorphic to \(Y\times Y\) but X is not homeomorphic to Y. This answers a question of V. Trnková [Proc. 5th Prague Topol. Symp. 1981, 631-641 (1983; Zbl 0501.54026)].

Reviewer: C.R.Borges

MSC:

54B10	Product spaces in general topology
54E35	Metric spaces, metrizability

Keywords:

countable metrizable spaces; homeomorphism

Citations:

Zbl 0501.54026