Full paper in PDF:
$%J. Taskinen, A continuous surjection from the unit interval onto the
unit square,
Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 1, 101–120.%$
We show that there exists a continuous surjection
which admits an
averaging operator in the sense of Pełczyński and which has the additional
property that the map
is an isomorphism from
onto a
subspace of
, where
.
1991 Mathematics Subject Classification: primary 46B20, secondary 54C05.