Pol (1996) and Arenas (1996) independently introduced transfinite extensions of finite order of mappings by the use of the length of a partially ordered set and Borst's order, respectively. By use of the transfinite order of mappings, Arenas introduced a transfinite dimension O-dim based on the Mori
✦ LIBER ✦
On Cantor manifolds for the large transfinite dimension
✍ Scribed by M. Reńska
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 134 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
✦ Synopsis
We construct metrizable Cantor manifolds for the transfinite extension of the Brouwer-Čech dimension tr Ind which are countable disjoint unions of Euclidean cubes and the irrationals. The construction is also simpler than constructions of metrizable Cantor manifolds for tr Ind published hitherto.
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