On βκ-normal spaces
Keywords:normal, almost normal, β-normal, βκ-normal, regular, almost regular, topological spaces
A topological space X is called βκ-normal if for every pair of disjoint regularly closed sets A and B, there exist disjoint open sets U and V of X such that = A, = B and ∩ = ∅. In this paper, we investigated a weaker form of normality called βκ-normality which is simultaneous generalization of normality, κ-normality and almost β-normality. Some new decomposition of normality is obtained in terms weakly β-normal spaces.
A. V. Arhangel’skii, “Relative topological properties and relative topological spaces”, Topology and its Applications, vol. 70, pp. 87-99, 1996.
A. V. Arhangel’skii and L. Ludwig, “On α-normal and β-normal spaces”, Commentationes Mathematicae Universitatis Carolinae, vol. 43, no. 3, pp. 507-519, 2001.
A. V. Arhangel’skii, Topological function spaces. Boston: Kluwer Academic Publishers, 1992.
P. Bhat and A.K. Das, “On some generalizations of normality”, Journal of Advanced Studies in Topology, vol. 6, no. 4, pp. 129-134, 2015. https://doi.org/10.20454/jast.2015.988
R. L. Blair, “Spaces in which special sets are z-embedded”, Canadian Journal of Mathematics, vol. 28, no. 4, pp. 673-690, 1976. https://doi.org/10.4153/CJM-1976-068-9
A. Császár, General Topology. Bristol: Adam Higler Ltd, 1978.
A. K. Das, “∆-normal spaces and decomposition of normality”, Applied General Topology, vol. 10, no. 2, pp. 197-206, 2009.
A. K. Das, “A note on spaces between normal and κ-normal spaces”, Filomat, vol. 27, no. 1, pp. 85-88, 2013.
A. K. Das, P. Bhat and J.K. Tartir, “On a Simultaneous of β-normality and almost normality”, Filomat, vol. 31, no. 1, pp. 425-430, 2017.
J. Dontchev, “Survey on pre-open sets”, The Proceedings of the Yatsushiro Topological Conference, pp. 1-18, 1998.
E. Ekici, “On γ-normal spaces”, Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, vol. 98, no. 3, pp. 259-272, 2007.
L. N. Kalantan, “π-normal topological spaces”, Filomat, vol. 22, no. 1, pp. 173-181, 2008.
L. N. Kalantan, “Results about κ-normality”, Topology and its Applications, vol. 125, no. 1, pp. 47-62, 2002. https://doi.org/10.1016/S0166-8641(01)00258-9
J. K. Kohli and A. K. Das, “New normality axioms and decompositions of normality”, Glasnik Matematicki., vol. 37, no. 57, pp. 165-175, 2002.
J. K. Kohli and A. K. Das, “On functionally θ-normal spaces”, Applied General Topology, vol. 6, no. 1, pp. 1-14, 2005. https://doi.org/10.4995/agt.2005.1960
J. K. Kohli and A. K. Das, “A class of spaces containing all generalized absolutely closed (almost compact) spaces”, Applied General Topology, vol. 7, no. 2, pp. 233-244, 2006. https://doi.org/10.4995/agt.2006.1926
K. Kuratowski, “Topologie I”. New York: Hafner, 1958.
M. N. Mukherjee and D. Mandal, “On countably nearly paracompact spaces”, Matematički Vesnik, vol. 66, no. 3, pp. 265-273, 2014.
M. N. Mukherjee adn A. Debray, “On nearly paracompact spaces and nearly full normality”, Matematički Vesnik, vol. 50, pp. 99-104, 1998.
E. Murtinova, “A β-normal Tychonoff space which is not normal”, Commentationes Mathematicae Universitatis Carolinae, vol. 43, no. 1, pp. 159-164, 2002.
M. K. Singal and S. P. Arya, “Almost normal and almost completely regular spaces, Glasnik Matematicki, vol. 5, no. 25, pp. 141-152, 1970.
M. K. Singal and S. P. Arya, “On almost regular spaces”, Glasnik Matematicki., vol. 4, no. 25, pp. 88-99, 1969.
M. K. Singal and A. R. Singal, “Mildly normal spaces”, Kyungpook Mathematical Journal, vol. 13, pp. 27-31, 1973.
E. V. Shchepin, “Real valued functions, and spaces close to normal”, Siberian Mathematical Journal, vol. 13, no. 5, pp. 1182-1196, 1972. https://doi.org/10.1007/BF00968394
E. V. Shchepin, “On topological products, groups, and a new class od spaces more general than metric spaces”, Soviet Mathematics Doklady, vol. 17, no. 1, pp. 152-155, 1976.
L. A. Steen and J. A. Seebach, Counterexamples in topology. New York: Rinehart and Winston, Inc., 1970.
B. K. Tyagi, S. Singh and M. Bhardwaj, “bβ-connectedness as a simultaneous characterization of β-connectedness, γ-connectedness and ββ-connectedness”, Questions and Answers in General Topology, vol. 37, no. 2, pp. 135-153, 2019.
N. V. Veličko, “H-closed topological spaces”, American Mathematical Society Translations, vol. 78, no. 2, pp. 103-118, 1968. https://doi.org/10.1090/trans2/078/05
How to Cite
Copyright (c) 2023 Sumit Singh, Manoj Kumar Rana
This work is licensed under a Creative Commons Attribution 4.0 International License.
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.