On isbell’s density theorem for bitopological pointfree spaces II
-
M. Andrew Moshier
and
Joanne Walters-Wayland
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.
(Communicated by David Buhagiar)
References
[1] Banaschewski, B.—Brümmer, G. C. L.—Hardie, K. A.: Biframes and bispaces, Quaest. Math. 6 (1983), 13–25.10.1080/16073606.1983.9632289Search in Google Scholar
[2] Banaschewski, B.—Pultr, A.: Booleanization, Cahiers Topologie Géom. Différentielle Catég. 37 (1996), 41–60.Search 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/s10485-009-9209-0Search in Google Scholar
[4] Isbell, J.: Atomless parts of spaces, Math. Scand. 31 (1972), 5–32.10.7146/math.scand.a-11409Search 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.Search 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.2019.106962Search in Google Scholar
[7] Johnstone, P. T.: Stone Spaces. Cambridge Stud. Adv. Math., Vol. 3, Cambridge University Press, 1982.Search in Google Scholar
[8] Nxumalo, M. S.: Remoteness in the Category of Locales PhD Thesis, University of South Africa, 2023.Search in Google Scholar
[9] Picado, J.—Pultr, A.: Frames and Locales: Topology without Points. Front. Math., vol. 28, Springer, Basel, 2012.10.1007/978-3-0348-0154-6Search 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.2014.02.012Search in Google Scholar
[11] Schauarte, A: Biframes, PhD Thesis, McMaster University, 1992.Search in Google Scholar
[12] Suarez, A. L.: The Booleanization of a d-frame, Appl. Categ. Struct. 30 (2022), 485–497.10.1007/s10485-021-09663-9Search in Google Scholar
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Articles in the same Issue
- Joins of normal matrices, their spectrum, and applications
- On isbell’s density theorem for bitopological pointfree spaces II
- Every positive integer is a sum of at most n + 2 centered n-gonal numbers
- A generalisation of q-additive functions
- Generalised class groups in dihedral and fake ℤp-extensions
- Singular value bounds with applications to norm and numerical radius inequalities
- Coefficient bounds for convex functions associated with cosine function
- On solutions to q-difference equations for q-appell functions in the spirit of Olsson and Exton
- Numerical implementation of solving a boundary value problem including both delay and parameter
- Solutions of second order iterative boundary value problems with nonhomogeneous boundary conditions
- Global attractivity of nonlinear delay dynamic equations on time scales via Lyapunov functional method
- On pseudo almost periodic solutions of the parabolic-elliptic Keller-Segel systems
- A note on derivations into annihilators of the ideals of banach algebras
- Characterization of nonlinear mixed skew lie and jordan n-Type derivation on ∗-Algebras
- Linear and uniformly continuous surjections between Cp-spaces over metrizable spaces
- A goodness-of-fit test for testing exponentiality based on normalized dynamic survival extropy
- Monotonicity results of ratio between two normalized remainders of Maclaurin series expansion for square of tangent function
