New separation axioms in generalized bitopological spaces

Abstract

Here, we have studied the ideas of (s, t)-$$g_{\rho }$$ and (s, t)-$$\lambda _{\rho }$$-closed sets $$(s,t=1,2;\,\, s\not =t)$$ and pairwise $$\lambda$$-closed sets in a generalized bitopological space $$(X,{\rho_{1}}, {\rho_{2}})$$. We have investigated the properties on some new separation axioms namely pairwise $$T_\frac{1}{4}$$, pairwise $$T_\frac{3}{8}$$, pairwise $$T_\frac{5}{8}$$ and have established mutual relations with pairwise $$T_0$$, pairwise $$T_\frac{1}{2}$$ and pairwise $$T_1$$. Also we have shown that under certain conditions, these axioms are equivalent.