Scattered and paracompact order topologies

Gerald Kuba

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arXiv · 2005.09368

Scattered and paracompact order topologies

Gerald Kuba

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Abstract

We show that (in ZFC) every infinite set S can be equipped with 2^|S| complete metrics which generate mutually non-homeomorphic scattered order topologies on S. Furthermore, we show that (in ZFC) every uncountable set S can be equipped with 2^|S| mutually non-homeomorphic scattered and compact order topologies. (This would be unprovable in ZFC for countably infinite S.) In both enumeration theorems the cardinality 2^|S| is optimal.

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Gerald Kuba. 2020-05-19. Scattered and paracompact order topologies. https://arxiv.org/abs/2005.09368

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