Rationals with exotic convergences. II.

Roman Frič

Displaying similar documents to “Rationals with exotic convergences. II.”

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...

Coarse sequential convergence in groups, etc

Roman Frič, Fabio Zanolin (1990)

Czechoslovak Mathematical Journal

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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 $B (ℝ)$ .