Continuous images of Cantor's ternary set
Dynamical Systems
2017-10-24 v2 General Topology
Abstract
The Hausdorff-Alexandroff Theorem states that any compact metric space is the continuous image of Cantor's ternary set . It is well known that there are compact Hausdorff spaces of cardinality equal to that of 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 . Here we present a compact countably infinite non-Hausdorff space which is not the continuous image of Cantor's ternary set.
Keywords
Cite
@article{arxiv.1303.3810,
title = {Continuous images of Cantor's ternary set},
author = {Fabian Dreher and Tony Samuel},
journal= {arXiv preprint arXiv:1303.3810},
year = {2017}
}