## Square root of R^3

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Asking cute questions is great.

Answering such questions is a nice challenge.

An article by Mark Dominus about this topics is here ( EN ).

Solution in "*R*^{3} Has No Root", Robbert Fokkink, *American Mathematical Monthly* vol 109 March 2002, p. 285, uses the orientation preserving and reversing arguments.

Topological proof is in "Another Proof That *R*^{3} Has No Square Root", Sam B. Nadler, Jr., *American Mathematical Monthly* vol 111 June–July 2004, pp. 527–528.

Any idea for some new proof???

By the way in "The cartesian product of a certain nonmanifold and a line is *E*^{4}", R.H. Bing, *Annals of Mathematics* series 2 vol 70 1959 pp. 399–412, is a construction of a strange space B such that B x *R*^{ = }*R*^{4.}

GREAT RESULT !!!