Abstract
Some properties of regular and normal bitopological spaces are established. The classes of sets inheriting the bitopological properties of regularity and normality are found. A theorem on a finite covering of pairwise normal spaces is proved. We also study the behavior of individual multivalued mappings, taking the axioms of bitopological regularity and normality into account.
Similar content being viewed by others
References
J. C. Kelly, “Bitopological spaces,” Proc. London Math. Soc., 9(13), 71–89 (1963).
B. P. Dvalishvili, “Bitopological spaces: theory, relations with generalized algebraic structures and applications,” Math. Stud., 199 (2005).
H. P. A. Künzi, “Nonsymmetric topology,” Colloq. Math. Soc. Janos Boyai Math. Stud., 4, 303–308 (1995).
R. Engelking, General Topology [Russian translation], Mir, Moscow (1986).
R. D. Kopperman, “Asymmetry and duality in topology,” Topol. Appl., 66, 1–39 (1995).
B. S. Burdick, “Compactness and sobriety in bitopological spaces,” in: Topol. Proc. Summer 22 (1997), pp. 43–61.
I. E. Cooke and I. L. Reilly, “On bitopological compactness,” J. London Math. Soc., 9, 518–522 (1975).
B. P. Dvalishvili, “On some compactness types and separation axioms of bitopological spaces,” Bull. Georg. SSR Acad. Sci., 80(2), 289–292 (1975).
J. Ferrer, V. Gregori, and C. Alegre, “A note on pairwise normal spaces,” Indian J. Pure Appl. Math., 24, 595–601 (1993).
I. J. Dochviri, “One covering property of pairwise normal bitopological spaces,” in: Abstr. IV Congr. Georg. Math., 47 (2005).
V. I. Ponomarev, “Properties of topological spaces preserved under multivalued continuous mappings,” Russ. Mat. Sb., 51, No. 93, 515–536 (1960).
P. Fletcher, H. B. Hoyle, and C. W. Patty, “The comparison of topologies,” Duke Math. J., 36, 325–331 (1969).
S. Lal, “Pairwise concepts in bitopological spaces,” J. Austral. Math. Soc., Ser. A, 26, 241–250 (1978).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1720–1724, December, 2006.
Rights and permissions
About this article
Cite this article
Dochviri, I. Some comments on regular and normal bitopological spaces. Ukr Math J 58, 1955–1960 (2006). https://doi.org/10.1007/s11253-006-0180-8
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11253-006-0180-8