Abstract
We study relative normality properties in locales. We identify localic maps that preserve and ones that reflect various relative normality properties.
Dube was supported by the National Research Foundation of South Africa under Grant No. 113829.
(Communicated by Aleš Pultr)
References
[1] Archangel’skii, A. V.: Relative topological properties and relative topological spaces, Topology Appl. 70 (1996), 1325–1346.10.1016/0166-8641(95)00086-0Search in Google Scholar
[2] Archangel’skii, A. V.—Genedi, H. H. M.: Beginnings of the theory of relative properties. In: General Topology. Spaces and Mappings, MGU, Moscow, 1989, pp. 3–48.Search in Google Scholar
[3] Aull, C. E.: Embeddings extending various types of disjoint sets, Rocky Mountain J. Math. 14 (1984), 319–330.10.1216/RMJ-1984-14-2-319Search in Google Scholar
[4] Ball, R. N.—Walters-Wayland, J.: C- and C∗-quotients in pointfree topology, Dissertationes Math. (Rozprawy Mat.) 412 (2002), 62 pp.10.4064/dm412-0-1Search in Google Scholar
[5] Banaschewski, B.—Dube, T.—Gilmour, C.—Walters-Wayland, J.: Oz in pointfree topology, Quaest. Math. 32 (2009), 215–227.10.2989/QM.2009.32.2.4.797Search in Google Scholar
[6] Clementino, M. M.—Picado, J.—Pultr, A.: The other closure, Appl. Categ. Structures 26 (2018), 891–906.10.1007/s10485-018-9516-4Search in Google Scholar
[7] Dube, T.—Robat Sarpoushi, M.: On densely normal locales, Topology Appl. 275 (2020), 107015.10.1016/j.topol.2019.107015Search in Google Scholar
[8] Dube, T.—Walters-Wayland, J.: Coz-onto frame maps and some applications, Appl. Categ. Structures 15 (2007), 119–133.10.1007/s10485-006-9022-ySearch in Google Scholar
[9] Ferreria, M. J.—Gutiérrez García, J.—Picado, J.: Completely normal frames and real-valued functions, Topology Appl. 156 (2009), 2932–2941.10.1016/j.topol.2008.12.042Search in Google Scholar
[10] Gutiérrez García, J.—Kubiak, T.—Picado, J.: On hereditary properties of extremally disconnected frames and normal frames, Topology Appl., to appear.10.1016/j.topol.2019.106978Search in Google Scholar
[11] Gutiérrez García, J.—Picado, J.: On the parallel between normality and extremal disconnectedness, J. Pure Appl. Algebra 218 (2014), 784–803.10.1016/j.jpaa.2013.10.002Search in Google Scholar
[12] Hoshina, T.—Yamazaki, K.: Weak C-embedding and P-embedding, and product spaces, Topology Appl. 125 (2002), 233–247.10.1016/S0166-8641(01)00275-9Search in Google Scholar
[13] Johnstone, P. T.: Stone Spaces, Cambridge Univ. Press, Cambridge, 1982.Search in Google Scholar
[14] Picado, J.— Pultr, A.: Frames and Locales: Topology without Points. Front. Math., Birkhauser/Springer, Basel AG, Basel, 2012.10.1007/978-3-0348-0154-6Search in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular papers
- Some relative normality properties in locales
- Upper bounds of some special zeros for the Rankin-Selberg L-function
- Factorization of polynomials over valued fields based on graded polynomials
- Varieties of ∗-regular rings
- On reverse Hölder and Minkowski inequalities
- Coefficient inequalities related with typically real functions
- Existence of wandering and periodic domain in given angular region
- The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
- Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
- Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
- Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
- 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
- More on closed non-vanishing ideals in CB(X)
- The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
- Multi-opponent James functions
- An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
- A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
- On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
- Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
Articles in the same Issue
- Regular papers
- Some relative normality properties in locales
- Upper bounds of some special zeros for the Rankin-Selberg L-function
- Factorization of polynomials over valued fields based on graded polynomials
- Varieties of ∗-regular rings
- On reverse Hölder and Minkowski inequalities
- Coefficient inequalities related with typically real functions
- Existence of wandering and periodic domain in given angular region
- The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*
- Uniqueness problem of meromorphic mappings of a complete Kähler manifold into a projective space
- Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces
- Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces
- 𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms
- More on closed non-vanishing ideals in CB(X)
- The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data
- Multi-opponent James functions
- An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications
- A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models
- On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation
- Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations