## 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).

### MSC:

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

### Keywords:

sequential convergence; $$\ell$$-groups; kernel; sequences

Zbl 0681.06007
Full Text:

### References:

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