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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
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Problem about the existence of a continuous surjective map [closed]
Let $F$ be a closed set in $\Bbb R^2$, $F\neq \varnothing,\Bbb R^2$, and $F^\circ\neq \varnothing$,
does there exist a continuous surjective map from $\Bbb R\times \Bbb Z$ to $F^{\circ-}-F^\circ$?