To the theory of H-sober spaces. II
https://doi.org/10.26907/2949-3919.2024.2.70-83
Abstract
We show that generalized sobrifications of approximation spaces are homeomorphic to spaces of special basic ideals of the given spaces. Using this characterization, we generalize a series of known results on sobrifications of approximation spaces.
Supporting agencies: The work is supported by the Russian Science Foundation, project no. 24-21-00227.
About the Authors
M. I. Kudryashova
Novosibirsk State University
Russian Federation
Maria Igorevna Kudryashova
Russian Federation
Maria Igorevna Kudryashova
1 Pirogov str., Novosibirsk 630090, Russia
M V. Schwidefsky
Kazan Federal University;
Novosibirsk State University;
Sobolev Institute of Mathematics SB RAS,
Russian Federation
Marina Vladimirovna Schwidefsky
Russian Federation
Marina Vladimirovna Schwidefsky
18 Kremlyovskaya str., Kazan 420008, Russia;
1 Pirogov str., Novosibirsk 630090, Russia;
4 Acad. Koptyug Ave., Novosibirsk 630090, Russia
References
1. X. Xu, On H-sober spaces and H-sobrifi ations of T0-spaces, Topology Appl. 289, article no. 107548, 37pp. (2021). DOI: https://doi.org/10.1016/j.topol.2020.107548
2. G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove, D.S. Scott, Continuous lattices and domains, Encyclopedia Math. Appl. 93, Cambridge Univ. Press, Cambridge, 2003. DOI: https://doi.org/10.1017/CBO9780511542725
3. Yu.L. Ershov, On d-spaces, Theoret. Comput. Sci. 224 (1–2), 59–72 (1999). DOI: https://doi.org/10.1016/S0304-3975(98)00307-7
4. Yu.L. Ershov, Solimit points and u-extensions, Algebra and Logic 56 (4), 295–301 (2017). DOI: https://doi.org/10.1007/s10469-017-9450-9
5. M.I. Kudryashova, M.V. Schwidefsky, To the theory of H-sober spaces, Siberian Math. J. 65 (4) (2024).
6. Yu.L. Ershov, Topology for discrete mathematics, Publishing House SB RAS, Novosibirsk, 2020 [in Russian].
7. Yu.L. Ershov, The d-rank of an α-space does not exceed 1, Algebra and Logic 58 (6), 470–474 (2019). DOI: https://doi.org/10.1007/s10469-020-09566-z
8. J. Goubault-Larrecq, Non-Hausdorff topology and domain theory: selected topics in pointset topology, New Math. Monogr. 22, Cambridge Univ. Press, Cambridge, 2013. DOI: https://doi.org/10.1017/CBO9781139524438
9. Yu.L. Ershov, The d-rank of a topological space, Algebra and Logic 56 (2), 98–107 (2017). DOI: https://doi.org/10.1007/s10469-017-9432-y
10. Yu.L. Ershov, Theory of domains and nearby, in: “Formal methods in programming and their applications”, Lecture Notes in Computer Science 735, 1–7 (2005). DOI: https://doi.org/10.1007/BFb0039696
Review
For citations:
Kudryashova M.I., Schwidefsky M.V. To the theory of H-sober spaces. II. Mathematics and Theoretical Computer Science. 2024;2(2):70-83. (In Russ.) https://doi.org/10.26907/2949-3919.2024.2.70-83
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