The interacting boson models, and were used to perform a complete study of even –even 160-168Yb isotopes .The low –lying positive parity states, dynamic symmetries, reduced electric quadrupole transition probability , quadruple momentum , and potential energy surface for 160-168Yb were investigated. Energy level sequences and energy ratios showed the gradual transition of the properties of these nuclei from the γ-unstable features to the rotational features . Adding the pairing parameter to Hamiltonian had a very slight effect on this feature, but it raised the β band, since it represents symmetry breaking such as in γ-unstable features . This applies to the experimental decay scheme of 160-168Yb isotopes. In , proton and neutron quadruple deformation parameters and showed values equal to -1.24 and approximately 0.7, respectively, which supports the same idea in the interacting boson model . A contour plot of the potential energy surface for 160-168Yb isotopes showed that the minimum potential occurs at approximately .
In this paper, we introduce new classes of sets called g *sD -sets , g *sD −α -sets , g *spreD − sets , g *sbD − -sets and g *sD −β -sets . Also, we study some of their properties and relations among them . Moreover, we use these sets to define and study some associative separation axioms .
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