## A piecewise Toronto space

**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

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