On sheaves of Abelian groups and universality
Keywords:sheaves, universal sheaves, universal spaces, containing spaces, saturated classes of spaces
Universal elements are one of the most essential parts in research fields, investigating if there exist (or not) universal elements in different classes of objects. For example, classes of spaces and frames have been studied under the prism of this universality property. In this paper, studying classes of sheaves of Abelian groups, we construct proper universal elements for these classes, giving a positive answer to the existence of such elements in these classes.
G. E. Bredon, Sheaf Theory, McGraw-Hill, New York, 1967
T. Dube, S. Iliadis, J. van Mill and I. Naidoo, Universal frames, Topology and its Applications 160, no. 18 (2013), 2454-2464. https://doi.org/10.1016/j.topol.2013.07.039
D. N. Georgiou, S. D. Iliadis and A. C. Megaritis, On base dimension-like functions of the type Ind, Topology and its Applications 160, no. 18 (2013), 2482-2494. https://doi.org/10.1016/j.topol.2013.07.042
D. N. Georgiou, S. D. Iliadis, A. C. Megaritis and F. Sereti, Universality property and dimension for frames, Order 37, no. 3 (2019), 427-444. https://doi.org/10.1007/s11083-019-09513-3
D. N. Georgiou, S. D. Iliadis, A. C. Megaritis and F. Sereti, Small inductive dimension and universality on frames, Algebra Universalis 80, no. 2 (2019), 21-51. https://doi.org/10.1007/s00012-019-0593-5
P. S. Gevorgyan, S. D. Iliadis and Yu V. Sadovnichy, Universality on frames, Topology and its Applications 220 (2017), 173-188. https://doi.org/10.1016/j.topol.2017.02.010
S. D. Iliadis, A construction of containing spaces, Topology and its Applications 107 (2000), 97-116. https://doi.org/10.1016/S0166-8641(00)90095-6
S. D. Iliadis, Mappings and universality, Topology and its Applications 137, no. 1-3 (2004), 175-186. https://doi.org/10.1016/S0166-8641(03)00207-4
S. D. Iliadis, Universal Spaces and Mappings, North-Holland Mathematics Studies 198, Elsevier, 2005.
S. D. Iliadis, On isometrically universal spaces, mappings, and actions of groups, Topology and its Applications 155, no. 14 (2008), 1502-1515. https://doi.org/10.1016/j.topol.2008.03.006
S. D. Iliadis, Universal elements in some classes of mappings and classes of G-spaces, Topology and its Applications 156, no. 1 (2008), 76-82. https://doi.org/10.1016/j.topol.2008.04.010
S. D. Iliadis, A separable complete metric space of dimension n containing isometrically all compact metric spaces of dimension n, Topology and its Applications 160, no. 11 (2013), 1271-1283. https://doi.org/10.1016/j.topol.2013.04.020
S. D. Iliadis and I. Naidoo, On isometric embeddings of compact metric spaces of a countable dimension, Topology and its Applications 160, no. 11 (2013), 1284-1291. https://doi.org/10.1016/j.topol.2013.04.021
S. D. Iliadis, On embeddings of topological groups, Fundamental and Applied Mathematics 20, no. 2 (2015), 105-112 (Russian). Journal of Mathematical Sciences 223, no. 6 (2017), 720-724 (English). https://doi.org/10.1007/s10958-017-3381-9
S. D. Iliadis, On isometric embeddings of separable metric spaces, Topology and its Applications 179 (2015), 91-98. https://doi.org/10.1016/j.topol.2014.08.019
S. D. Iliadis, Dimension and universality on frames, Topology and its Applications 201 (2016), 92-109. https://doi.org/10.1016/j.topol.2015.12.029
S. D. Iliadis, On spaces continuously containing topological groups, Topology and its Applications 272 (2020),107072. https://doi.org/10.1016/j.topol.2020.107072
S. D. Iliadis, On actions of spaces continuously containing topological groups, Topology and its Applications 275 (2020), 107035. https://doi.org/10.1016/j.topol.2019.107035
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