A piecewise Toronto space

Lajos Soukup

We show that it is consistent that there is a hereditarily separable, 0-dimensional $ T_2$ space space $ X$ of cardinality $ {\omega}_1$ such that for each uncountable subspace $ Y$ of $ X$ there is a continuous bijection $ {\varphi}:Y\to X$ and there is a partition $ (Y_i)_{i<n}$ of $ Y$ into finitely many pieces such that $ {\varphi}\restriction Y_i$ is homeomorphism for each $ i<n$.

Key words and phrases: Toronto space, homeomorphic, hereditarily separable, independent result, forcing, iterated forcing, piecewise

2000 Mathematics Subject Classification: 54E25, 03E35

Downloading the paper