Abstract:It is well known that if a poset satisfies Property A and its dual form, then the o-convergence and o2-convergence in the poset are equivalent. In this paper, we supply an example to illustrate that a poset in which the o-convergence and o2-convergence are equivalent may not satisfy Property A or its dual form, and carry out some further investigations on the equivalence of the o-convergence and o2-convergence. By introducing the concept of the local Frink ideals (the dually local Frink ideals) and establishin… Show more
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