On βκ-normal spaces
DOI:
https://doi.org/10.22199/issn.0717-6279-4277Keywords:
normal, almost normal, β-normal, βκ-normal, regular, almost regular, topological spacesAbstract
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.
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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
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