arXiv subjects
Publications and source records attributed to Jerzy Wojciechowski.
The longstanding conjecture of Halin characterizing the existence of normal spanning trees in infinite graphs has been recently proved by Max Pitz [3]. A critical step in the proof involves the construction of dominated torsos, whose properties are essential to the overall proof. In this note, we provide a correction to the proof of a key property of this construction.
Abstract. We provide a characterization of classes of filters $\mathbb{D}$ for which the full subcategory $\operatorname{fix}\operatorname{A}_{\mathbb D}$ of $\mathsf{Conv}$ formed by convergences determined by the adherence of filters of the class $\mathbb{D}$ is simple in $\mathsf{Conv}$. Along the way, we also elucidate when two classes of filters result in the same category of adherence-determined convergences. As an application of the main result, we show that the category of hypotopologies is not simple, thus answering a question from [25].
In this note it is proved 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, an example is given of a Hausdorff convergence with idempotent set adherence (subdiagonal convergence) that is not weakly diagonal.