A completion of $\mathbb {Z}$ is a field

José E. Marcos

Displaying similar documents to “A completion of $ℤ$ is a field”

Pointwise convergence fails to be strict

Ján Borsík, Roman Frič (1998)

Czechoslovak Mathematical Journal

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It is known that the ring $B (ℝ)$ of all Baire functions carrying the pointwise convergence yields a sequential completion of the ring $C (ℝ)$ of all continuous functions. We investigate various sequential convergences related to the pointwise convergence and the process of completion of $C (ℝ)$ . In particular, we prove that the pointwise convergence fails to be strict and prove the existence of the categorical ring completion of $C (ℝ)$ which differs from $B (ℝ)$ .

Rings of maps: sequential convergence and completion

Roman Frič (1999)

Czechoslovak Mathematical Journal

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The ring $B (R)$ of all real-valued measurable functions, carrying the pointwise convergence, is a sequential ring completion of the subring $C (R)$ of all continuous functions and, similarly, the ring $𝔹$ of all Borel measurable subsets of $R$ is a sequential ring completion of the subring $𝔹_{0}$ of all finite unions of half-open intervals; the two completions are not categorical. We study $ℒ_{0}^{*}$ -rings of maps and develop a completion theory covering the two examples. In particular, the $σ$ -fields of sets form...

Relatively coarse sequential convergence

Roman Frič, Fabio Zanolin (1997)

Czechoslovak Mathematical Journal

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We generalize the notion of a coarse sequential convergence compatible with an algebraic structure to a coarse one in a given class of convergences. In particular, we investigate coarseness in the class of all compatible convergences (with unique limits) the restriction of which to a given subset is fixed. We characterize such convergences and study relative coarseness in connection with extensions and completions of groups and rings. E.g., we show that: (i) each relatively coarse dense...

Displaying similar documents to “A completion of ℤ is a field”

Pointwise convergence fails to be strict

Rings of maps: sequential convergence and completion

Relatively coarse sequential convergence

Displaying similar documents to “A completion of $ℤ$ is a field”