space space 
of cardinality
such that
for each uncountable subspace 
of
there is a continuous bijection
and there is a
partition
of into finitely many pieces
such that
is homeomorphism for each 
.
Lajos Soukup
We show that it is consistent that there is a hereditarily separable,
0-dimensional space space of cardinality
such that
for each uncountable subspace of
there is a continuous bijection
and there is a
partition
of into finitely many pieces
such that
is homeomorphism for each .
Key words and phrases: Toronto space, homeomorphic, hereditarily separable, independent result, forcing, iterated forcing, piecewise
2000 Mathematics Subject Classification: 54E25, 03E35