Proper absolute extensor
Keywords:
absolute proper extensor for $n$-dimensional spaces, $\mathrm{DD}^{\mathrm{n}} \mathrm{P}$-property, $n$-dimensional Menger compactumAbstract
We describe the proper absolute (neighborhood) extensors for the class of at most $n$-dimensional spaces, notation $\mathrm{A}(\mathrm{N}) \mathrm{E}_{\mathrm{p}}(\mathrm{n})$. For example, the unique locally compact $n$-dimensional separable metric space $X \in \mathrm{AE}_{\mathrm{p}}(\mathrm{n})$ satisfiyng the $\mathrm{DD}^{\mathrm{n}}$ P-property is the space obtained by deleting a point from the $n$-dimensional Menger compactum. Non-metrizable $\mathrm{A}(\mathrm{N}) \mathrm{E}_{\mathrm{p}}(\mathrm{n})$-spaces are also described.
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