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Rings of maps: sequential convergence and completion and strictness

In: Tatra Mountains Mathematical Publications, vol. 14, no. 1
Roman Frič - Tsugunori Nogura
Detaily:
Rok, strany: 1998, 137 - 143
O článku:
The ring $B(\Bbb R)$ of all real-valued measurable functions, carrying the pointwise convergence is a sequential ring completion of the subring $C(\Bbb R)$ of all continuous functions and, similarly, the ring $\Scr B$ of all Borel measurable subsets of $\Bbb R$ is a sequential ring completion of the subring $\Scr B0$ of all finite unions of half-open intervals. We develop a completion theory for regular $L0*$-rings, in particular for rings of maps, and study the two examples in this context. We prove that $B(\Bbb R)$ and $\Scr B$ fail to be epireflections of the regular $L0*$-rings $C(\Bbb R)$ and $\Scr B0$, respectively, into the subcategory of all complete regular $L0*$-rings. We also discuss the productivity of strictness, a notion closely related to the regularity of $L0*$-spaces.
Ako citovať:
ISO 690:
Frič, R., Nogura, T. 1998. Rings of maps: sequential convergence and completion and strictness. In Tatra Mountains Mathematical Publications, vol. 14, no.1, pp. 137-143. 1210-3195.

APA:
Frič, R., Nogura, T. (1998). Rings of maps: sequential convergence and completion and strictness. Tatra Mountains Mathematical Publications, 14(1), 137-143. 1210-3195.