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λ*-closed sets and new separation axioms in Alexandroff spaces

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Here we have studied the ideas of $g^*$-closed sets, $g\wedge_\tau $-sets and $\lambda^*$-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff \cite{AD}. We have also studied some separation axioms like $ T_\frac{\omega}{4}, T_\frac{3\omega}{8}, T_\omega $ in Alexandroff spaces and also have introduced a new separation axiom namely $ T_\frac{5\omega}{8} $ axiom in this space.

Abstract

Here we have studied the ideas of $g^*$-closed sets, $g\wedge_\tau $-sets and $\lambda^*$-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff \cite{AD}. We have also studied some separation axioms like $ T_\frac{\omega}{4}, T_\frac{3\omega}{8}, T_\omega $ in Alexandroff spaces and also have introduced a new separation axiom namely $ T_\frac{5\omega}{8} $ axiom in this space.

참고문헌 (11)

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  4. Das, P., "Certain separation axioms in a space", Korean J. Math. Sciences, 7, pp.81~93 (2000)
  5. Das, P., "g-closed sets and a new separation axioms in Alexan-droff spaces", Archivum Mathematicum(BRNO)Tomus, 39, pp.299~307 (2003)
  6. Dunham, W, "T12-spaces", Kyungpook Math. J, 17(2), pp.161~169 (1977)
  7. Kelley, J. L, "Graduate Text in Mathematics" (1975), Springer-Verlag
  8. Lahiri B. K., "Semi-open set in a space", Sains Malaysiana, 24(4), pp.1~11 (1995)
  9. Levine, N., "Generalised closed sets in topology", Rend. Cire. Mat. Palermo, 19(2), pp.89~96 (1970)
  10. M. S. Sarsak, "Weak separation axioms in generalized topological spaces", Acta Math. Hungar., 131(1-2), pp.110~121 (2011)
  11. M. S. Sarsak, "New separation axioms in generalized topological spaces", Acta Math. Hungar, 132(3), pp.244~252 (2011)

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