Three Problems in Convergence Theory
Keywords:
convergence spaces, diagonal properties of convergence spaces, hypotopologies, initially dense convergences, paratopologiesAbstract
In this note, we prove that the class of paratopologies
is simple and that under the assumption that the measurable cardinals form a proper class, the class of hypotopologies is not simple. Moreover, we provide an example of a Hausdorff convergence with idempotent set adherence (subdiagonal convergence) that is not
weakly diagonal.
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