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

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).


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


Zbl 0681.06007
Full Text: EuDML


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