Lower separation axioms in bitopogenous spaces
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Tom Richmond
and
Josef Šlapal
Abstract
Several naturally defined lower separation axioms for bitopological spaces obtained by modifying the axioms T0, T1, and R0 appear in the literature. We introduce and study analogous separation axioms for bitopogenous spaces. In particular, we investigate relationships between the axioms and discuss the conditions under which the relationships are similar to those between the corresponding separation axioms for bitopological spaces.
The authors acknowledge the support by Brno University of Technology, the first author from the project MeMoV II no. CZ.02.2.69/0.0/0.0/18-053/0016962 and the second one from the Specific Research project no. FSI-S-23-8161.
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Communicated by L’ubica Holá
References
[1] Belaid, K.—Echi, O.—Lazaar, S.: T(α,β)-spaces and the Wallman compactification, Internat. J. Math. Math. Sci. 68 (2004), 3717–3735.10.1155/S0161171204404050Search in Google Scholar
[2] Burgess, D. C. J.—Fitzpatrick, M.: Syntopogenous preordered spaces, Math. Proc. Cambridge Philos. Soc. 80(1) (1976), 71–79.10.1017/S0305004100052683Search in Google Scholar
[3] Császár, Á.: Foundations of General Topology, Pergamon Press, Macmillan Company, NY, 1963.Search in Google Scholar
[4] Császár, Á.: Finite extensions of topogenities, Acta Math. Hungar. 89(1–2) (2000) 55–69.10.1023/A:1026725424906Search in Google Scholar
[5] Davis, A. S.: Indexed systems of neighborhoods for general topological spaces, Amer. Math. Monthly 68(9) (1961), 886–893.10.2307/2311686Search in Google Scholar
[6] Holgate, D.—Iragi, M.: Quasi-uniform and syntopogenous structures on categories, Topology Appl. 263 (2019), 16–25.10.1016/j.topol.2019.05.024Search in Google Scholar
[7] Lal, S.: Pairwise concepts in bitopological spaces, J. Austral. Math. Soc. Ser. A 2 6(2) (1978), 241–250.10.1017/S1446788700011733Search in Google Scholar
[8] McCluskey, A.—Künzi, H.-P.—Richmond, T.: Ordered separation axioms and the Wallman ordered compactification, Publ. Math. Debrecen 73(3–4) (2008), 361–377.10.5486/PMD.2008.4251Search in Google Scholar
[9] Misra, D. N.—Dube, K. K.: Pairwise R0-space, Annales de la Société Scientifique de Bruxelles 87(I) (1973), 3–15.Search in Google Scholar
[10] Mršević, M.: On pairwise R0 and pairwise R1 bitopological spaces, Bull. Math. Soc. Sci. Math. R. S. Roumanie 30(78) (1986), 141–148.Search in Google Scholar
[11] Murdeshwar, M. G.—Naimpally, S. A.: Quasi-Uniform Topological Spaces, Noordhoof, 1966.Search in Google Scholar
[12] Reilly, I.: On pairwise R0 spaces, Annales de la Société Scientifique de Bruxelles 88(III) (1974), 293–296.Search in Google Scholar
[13] Richmond, T.: General Topology: An Introduction, De Gruyter, Berlin, 2020.10.1515/9783110686579Search in Google Scholar
[14] šlapal, J.: A note on F-topologies, Math. Nachr. 141 (1989), 283–287.10.1002/mana.19891410126Search in Google Scholar
[15] šlapal, J.: On categories of ordered sets with a closure operator, Publ. Math. Debrecen 78(1) (2011), 61–69.10.5486/PMD.2011.4442Search in Google Scholar
[16] Swart, J.: Total disconnectedness in bitopological spaces and product bitopological spaces, Indag. Math. (Proceedings) 74 (1971), 135–145.10.1016/S1385-7258(71)80020-3Search in Google Scholar
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Articles in the same Issue
- Right algebras in Sup and the topological representation of semi-unital and semi-integral quantales, revisited
- Topological representation of some lattices
- Exact-m-majority terms
- Polynomials whose coefficients are generalized Leonardo numbers
- A study on error bounds for Newton-type inequalities in conformable fractional integrals
- Improved conditions for the distributivity of the product for σ-algebras with respect to the intersection
- Close-to-convex functions associated with a rational function
- Complete monotonicity for a ratio of finitely many gamma functions
- Class of bounds of the generalized Volterra functions
- Some new uniqueness and Ulam–Hyers type stability results for nonlinear fractional neutral hybrid differential equations with time-varying lags
- Existence of positive solutions to a class of boundary value problems with derivative dependence on the half-line
- Solving Fredholm integro-differential equations involving integral condition: A new numerical method
- Bounds of some divergence measures on time scales via Abel–Gontscharoff interpolation
- Weighted 1MP and MP1 inverses for operators
- Non-commutative effect algebras, L-algebras, and local duality
- Operator Bohr-type inequalities
- Some results for weighted Bergman space operators via Berezin symbols
- Lower separation axioms in bitopogenous spaces
- Fisher information in order statistics and their concomitants for Cambanis bivariate distribution
- Irreducibility of strong size levels
