Countable ordinal spaces and compact countable subsets of a metric space

27 Jul 2018 Álvarez-Samaniego Borys Merino Andrés

We show in detail that every compact countable subset of a metric space is homeomorphic to a countable ordinal number, which extends a result given by Mazurkiewicz and Sierpinski for finite-dimensional Euclidean spaces. In order to achieve this goal, we use Transfinite Induction to construct a specific homeomorphism... (read more)

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