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On isbell’s density theorem for bitopological pointfree spaces II

  • M. Andrew Moshier , Imanol Mozo Carollo EMAIL logo und Joanne Walters-Wayland
Veröffentlicht/Copyright: 9. Juni 2025
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Abstract

With the aim of studying subspaces in pointfree bitopology, we characterize extremal epimorphism in biframes and show that a smallest dense one always exists, providing an analogue of Isbell’s Density Theorem. Further we study the functoriality of assigning to each biframe its lattice of subbilocales and its smallest dense subbilocale.


The second named author acknowledges support from the Basque Government (grant IT1483-22).


  1. (Communicated by David Buhagiar)

References

[1] Banaschewski, B.—Brümmer, G. C. L.—Hardie, K. A.: Biframes and bispaces, Quaest. Math. 6 (1983), 13–25.10.1080/16073606.1983.9632289Suche in Google Scholar

[2] Banaschewski, B.—Pultr, A.: Booleanization, Cahiers Topologie Géom. Différentielle Catég. 37 (1996), 41–60.Suche in Google Scholar

[3] Ferreira, M. J.—Gutiérrez García, J.—Picado, J.: Insertion of continuous real functions on spaces, bispaces, ordered spaces and pointfree spacesA common root, Appl. Categ. Struct. 19 (2011), 469–487.10.1007/s10485-009-9209-0Suche in Google Scholar

[4] Isbell, J.: Atomless parts of spaces, Math. Scand. 31 (1972), 5–32.10.7146/math.scand.a-11409Suche in Google Scholar

[5] Jung, A.—Moshier, M. A.: On the bitopological nature of Stone duality, Technical Report CSR-06-13, School of Computer Science, The University of Birmingham, 2006.Suche in Google Scholar

[6] Moshier, M. A.—Mozo Carollo, I.—Walters-Wayland, J.: On Isbell’s density theorem for bitopological pointfree spaces I, Topology Appl. 273 (2020), Art. ID 106962.10.1016/j.topol.2019.106962Suche in Google Scholar

[7] Johnstone, P. T.: Stone Spaces. Cambridge Stud. Adv. Math., Vol. 3, Cambridge University Press, 1982.Suche in Google Scholar

[8] Nxumalo, M. S.: Remoteness in the Category of Locales PhD Thesis, University of South Africa, 2023.Suche in Google Scholar

[9] Picado, J.—Pultr, A.: Frames and Locales: Topology without Points. Front. Math., vol. 28, Springer, Basel, 2012.10.1007/978-3-0348-0154-6Suche in Google Scholar

[10] Picado, J.—Pultr, A.: (Sub)fit biframes and non-symmetric nearness, Topology Appl. 168 (2014), 66–81.10.1016/j.topol.2014.02.012Suche in Google Scholar

[11] Schauarte, A: Biframes, PhD Thesis, McMaster University, 1992.Suche in Google Scholar

[12] Suarez, A. L.: The Booleanization of a d-frame, Appl. Categ. Struct. 30 (2022), 485–497.10.1007/s10485-021-09663-9Suche in Google Scholar

Received: 2024-10-04
Accepted: 2025-01-16
Published Online: 2025-06-09
Published in Print: 2025-06-26

© 2025 Mathematical Institute Slovak Academy of Sciences

Heruntergeladen am 15.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0036/html
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