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arXiv · 1303.3810

Continuous images of Cantor's ternary set

Fabian Dreher·Tony Samuel
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Abstract

The Hausdorff-Alexandroff Theorem states that any compact metric space is the continuous image of Cantor's ternary set $C$. It is well known that there are compact Hausdorff spaces of cardinality equal to that of $C$ that are not continuous images of Cantor's ternary set. On the other hand, every compact countably infinite Hausdorff space is a continuous image of $C$. Here we present a compact countably infinite non-Hausdorff space which is not the continuous image of Cantor's ternary set.

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Fabian Dreher, Tony Samuel. 2013-03-15. Continuous images of Cantor's ternary set. https://arxiv.org/abs/1303.3810

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