On Products of CAUCHY Completions
β Scribed by D. C. Kent; R. Ruiz de Eguino
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 540 KB
- Volume
- 155
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We investigate conditions under which the completion of a product of CAUCHY spaces is equivalent to the product of the completions. Necessary and sufficient conditions are given for the WYLER completion to commute with products. The natural completion and natural ordered completion are shown to commute with finite products.
π SIMILAR VOLUMES
## Abstract It is consistent with constructive set theory (without Countable Choice, clearly) that the Cauchy reals (equivalence classes of Cauchy sequences of rationals) are not Cauchy complete. Related results are also shown, such as that a Cauchy sequence of rationals may not have a modulus of c