Full paper in PDF:
$%J. Taskinen, A continuous surjection from the unit interval onto the unit square, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 1, 101–120.%$

A Continuous Surjection from the Unit Interval Onto the Unit Square
Jari TASKINEN
Department of Mathematics
University of Helsinki
Hallituskatu 15
SF-00100 Helsinki — Finland

Received: August 28, 1992
Revised: December 10, 1992
ABSTRACT

We show that there exists a continuous surjection f:I --> I2 which admits an averaging operator in the sense of Pełczyński and which has the additional property that the map o f :f '--> f o f is an isomorphism from 2 Lp(I ) onto a subspace of Lp(I) , where 1< p <8 .

1991 Mathematics Subject Classification: primary 46B20, secondary 54C05.