On some types of kernels of a convergence \(l\)-group. (English) Zbl 0748.06006

Jakubík, Ján

Czech. Math. J. 39(114), No. 2, 239-247 (1989).

The system \(\text{Conv} G\) of all sequential convergences in an \(\ell\)- group was introduced and investigated by the reviewer [Czech. Math. J. 39(114), No. 2, 232-238 (1989; Zbl 0681.06007)]. If \(p\) is a condition concerning \(\ell\)-groups, then the \(p\)-kernel of \(G\) is defined to be the largest element of the system of all convex \(\ell\)-subgroups of \(G\) which satisfy the condition \(p\) (if such a largest element does exist). In the present paper the author studies the existence of kernels corresponding to a series of conditions related to properties of sequences. In the reviewer’s paper quoted above it was assumed that the Urysohn’s Axiom was satisfied; the results of the present paper remain valid without this axiom (though the author does not mention this fact explicitly).

Reviewer: M.Harminc (Košice)

MSC:

06F15	Ordered groups
06F20	Ordered abelian groups, Riesz groups, ordered linear spaces

Keywords:

sequential convergence; \(\ell\)-groups; kernel; sequences

Citations:

Zbl 0681.06007

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