### On co-Filters in Semigroups with Apartness

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**Authors:**D. A. ROMANO

**DOI:**10.46793/KgJMat2104.607R

**Abstract:**

The logical environment of this research is the Intuitionistic Logic and principled-philosophical orientation of the Bishop’s Constructive Mathematics. In this paper, basing our consideration on the sets with the apartness relation, we analyze the lattices of all co-ﬁlters of an ordered semigroup under a co-quasiorder as a continuation of our article [?]. We prove a number of results related to co-ﬁlters in a semigroup with apartness and the lattice of all co-ﬁlters of such semigroups.

**Keywords:**

Bishop’s constructive mathematics, semigroup with apartness, co-order and co-quasiorder relations, co-ﬁlters.

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