Abstract
The notions of α-normality and β-normality were introduced by Arhangel’skii and L. Ludwig [4]. In the present paper, we have investigated these concepts in relative sense, proved their dependency and independency on other versions of relative normality. Some relative versions of β normality are defined, their relations with various version of relative normality are discussed and it is observed that some absolute versions of normality coincide with normality in a class of relative variant of β-normal.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. V. Arhangel'skii and H. M. M. Genedi, The origin of the theory of relative topological properties, in: General Topology. Spaces and Mappings, MGU (Moscow, 1989), pp. 3-48 (in Russian)
Arhangel'skii, A.V.: A relative topological properties and relative topological spaces. Topology Appl. 70, 87-99 (1996)
Arhangel'skii, A.V.: Relative normality and dense subspaces. Topology Appl. 123, 27-36 (2002)
Arhangel'skii, A.V., Ludwig, L.: On \(\alpha \)-normal and \(\beta \)-normal spaces. Comment. Math. Univ. Carolin. 42, 507-519 (2001)
Blair, R.L.: Spaces in which special sets are \(z\)-embedded. Canad. Math. J. 28, 673-690 (1976)
A. K. Das, Pratibha Bhat and J. K. Tartir, On a simultaneous generalization of \(\beta \)-normality and almost normality, Filomat, 31 (2017), 425-430
A. K. Das and Pratibha Bhat, A class of spaces containing all densely normal spaces, Indian J. Math., 57 (2015), 217-224
Das, A.K.: A note on spaces between normal and \(\kappa \)-normal spaces. Filomat 27, 85-88 (2013)
Das, A.K.: \(\Delta \)-normal spaces and decompositions of normality. Appl. Gen. Topol. 10, 197-206 (2009)
Lutfi, N.: Kalantan, \(\pi \)-normal topological spaces. Filomat 22, 173-181 (2008)
K. Kuratowski, Topologie. I, Hafner (New York, 1958)
Sehar Shakeel Raina and A. K. Das, Some variants of normality in relative topological spaces, preprint
M. Singal and Asha Rani Singal, Mildly normal spaces, Kyungpook Math. J., 13 (1973), 27-31
Singal, M., Arya, S.: Almost normal and almost completely regular spaces. Kyungpook Math. J. 25, 141-152 (1970)
Singal, M., Arya, S.P.: On almost-regular spaces. Glas. Mat. Ser. III(4), 89-99 (1969)
Stchepin, E.V.: On topological products, groups and a new class of spaces more general than metric spaces. Soviet Math. Dokl. 17, 152-155 (1976)
Stchepin, E.V.: Real-valued functions and spaces close to normal. Sib. Math. J. 13, 1182-1196 (1972)
L. A. Steen and J. A. Seebach, Jr., Counterexamples in Topology, Springer Verlag (New York, 1978)
Veličko, N.V.: H-closed topological spaces. Trans. Amer. Math. Soc. 78, 103-118 (1968)
Willard, S.: General Topology, Addison-Wesley. Reading, Mass. (1970)
Zaitsev, V.: Some classes of topological spaces and their bicompact extensions. Dokl. Akad. Nauk SSSR 178, 778-779 (1968). (in Russian)
Author information
Authors and Affiliations
Corresponding author
Additional information
The second author is thankful to the Department of Science and Technology (DST), Government of India for awarding INSPIRE fellowship (IF160701).
Rights and permissions
About this article
Cite this article
Das, A.K., Raina, S.S. On relative β-normality. Acta Math. Hungar. 160, 468–477 (2020). https://doi.org/10.1007/s10474-019-01006-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-019-01006-4