1,720,964 research outputs found
The impact of Pontryagin and Bohr functors on large-scale properties of locally compact abelian groups
No full textFollowing the recent introduction of functorial coarse structures on groups, we consider functorial coarse structures on topological groups. In particular, we focus on the compact-group coarse structure and we study the impact of Pontryagin and Bohr functor in small-scale and large-scale properties of locally compact abelian groups. We provide results concerning both the covering dimension and the asymptotic dimension
Applications of dimension theory to embeddability problems in topological data analysis: the case study of the Gromov-Hausdorff distance
No full textZava N. Applications of dimension theory to embeddability problems in topological data analysis: the case study of the Gromov-Hausdorff distance / N. Zava // Algebraic and geometric methods of analysis - 2024 : abstr. of the Intern. sci. conf., Odesa, 27-30 May - 2024 / [Odesa Nat. Univ. of Technology et al.] ; sci comm.: [ Yu. Fedchenko, N. Konovenko et al.]. – Odesa, 2024. – P. 131. – Ref.: 1 tit
Weakly weighted generalised quasi-metric spaces and semilattices
No full textMotivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwise weakly weighted (generalised) quasi-metrics. We then systematise and extend to full generality the correspondences between these objects and other structures arising in theoretical computer science and dynamics. In particular, we study the correspondences with weak partial metrics and, if the underlying space is a semilattice, with invariant (generalised) quasi-metrics satisfying the descending path condition, and with strictly monotone semi(-co-)valuations. We conclude discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation of both the known intrinsic semilattice entropy and the semigroup entropy
Epimorphisms and closure operators of categories of semilattices
No full textMotivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLatt O of join semilattices with bottom element. In particular, we show that there are only finitely many closure operators of both categories, and provide a complete classification. We use this result to deduce the known fact that epimorphisms of SLatt and SLatt O are surjective. We complement the paper with two different proofs of this result using either generators or Isbell’s zigzag theorem
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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