engleski

Relative embeddability into Lipscomb?s 0-dimensional universal space

Let $\Sigma(\tau)$ be the generalized Sierpinski curve which is naturally identified with the Lipscomb's space $J(\tau)$. Then the set of irrational points of $\Sigma(\tau)$ is universal for 0-dimensional metric spaces of weight $\leq\tau$. We prove that any embedding of a compact subspace of a 0-dimensional metric space of dimension $\leq\tau$ into the set of irrational points of $\Sigma(\tau)$ can be extended to an embedding of the whole space.

covering dimension ; generalized Sierpinski curve ; universal space ; Lipscomb's universal space ; embedding

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